9P01_Motion_Avanti Module

9P01 – Motion 1 Fifth Edition 9P01. Motion TABLE OF CONTENTS 9P01. Motion 1 9P01.1 Distance, Displacement & Speed ………………….………………….………………….………………….……………….….2 9P01.2 Velocity & Acceleration ………………….………………….………………….………………….……………………………..….4 9P01.3 Graphical Representation of Motion & Uniform Circular Motion………………….……………………………….6 9P01.4 Equations of Motion ………………….………………….………………….………………….………………….………………….8 Advanced Practice Problems …………………….………………….………………….………………….………………………………..10 CBSE Practice Problems …………………….……….........………….………………….………………….………………………………..12 Olympiad Practice Problems …………………….……….........………….………………….…………...………………………………..15

9P01 – Motion 2 9P01.1 Distance, Displacement & Speed CONCEPTS COVERED 1. Description of a motion 2. Importance of frame of reference 3. Relative motion and its significance in real life 4. Difference between distance and displacement 5. Uniform and non-uniform motion 6. Speed IN CLASS EXERCISE Q1. How can we describe the location of an object? Q2. Differentiate between distance and displacement. Q3. A particle is moving in a circular path of radius ������. What will be its displacement after half a circle is completed? Q4. A particle travels three quarters of a circle of radius ������. What is the magnitude of its displacement? Q5. A farmer moves along the boundary of a square field of side 10 ������ in 40 ������ . What will be the magnitude of displacement of the farmer at the end of 2 min 20 s from his initial position? Q6. What is meant by uniform motion? Give an example. Q7. Define the term average speed. Q8. A car travels a certain distance with a speed of 50 ������������/ℎ������ and returns with a speed of 40 ������������/ℎ. Calculate the average speed for the whole journey. Q9. On a 100 ������������ track, a train travels the first 30 ������������ at a uniform speed of 30 ������������ /ℎ. How fast must the train travel the next 70 ������������ so as to average 40 ������������/ℎ for the entire trip? HOMEWORK Q1. With the help of a suitable example, explain the terms distance and displacement. Q2. An object is moving with a uniform speed in a circle of radius ������. Calculate the distance and displacement: I. When it completes half of the circle. II. When it completes a full circle. Q3. A body moves in a circle of radius ‘2������’. What is the distance covered and displacement of the body after 2 complete rounds? Q4. An athlete completes one round of a circular track of diameter 200 ������ in 40 ������. What will be the distance covered and the displacement at the end of 2 min 20 ������? Q5. An ant climbs up five stairs, each of width 20 ������������ and height 20 ������������. Find the distance covered and displacement of ant, if it starts from the bottom, and reaches the start of the sixth staircase. 9P01.1

9P01 – Motion 3 Q6. What is non-uniform motion? Give some examples. Q7. Does the speedometer of a car measure its average speed? Q8. Abdul, while driving to school, computes the average speed for his trip to be 20 ������������/ℎ������. On his return trip along the same route, there is less traffic and the average speed is 40 ������������/ℎ������. What is the average speed for Abdul’s entire trip? Q9. A boy runs for 10 minutes at a uniform speed of 9 ������������/ℎ. At what speed should he run for the next 20 minutes so that the average speed becomes 12 ������������/ℎ? ADVANCED QUESTIONS Q1. A bridge is 500 ������ long. A 100 ������ long train crosses the bridge at a speed of 20 ������/������. The time taken by train to cross it will be: A) 25 ������ B) 5 ������ C) 30 ������ D) 20 ������ Q2. A body covers one-third of its journey with speed ������, next third with speed ������ and the last third with speed ������. Calculate the average speed of the body over the entire journey. Q3. A man can row a boat at 1.8 ������������������ℎ in still water. He heads straight downstream for 2.7������������ in a river where the current is 0.9 ������������������ℎ and then returns to the starting point. Calculate the time for the round trip. 9P01.1

9P01 – Motion 4 9P01.2 Velocity & Acceleration CONCEPTS COVERED 1. Definition of velocity 2. Calculation of velocity from displacement 3. Average and instantaneous velocity 4. Definition of acceleration 5. Positive and negative acceleration 6. Uniform and non-uniform acceleration IN CLASS EXERCISE Q1. Define the term velocity. What is its SI unit? Is it a scalar or vector quantity? Q2. Joseph jogs from one end ������ to the other end ������ of a straight 300 ������ road in 2 min 30 ������ and then turns around and jogs 100 ������ back to point ������ in another 50 ������. What are Joseph’s average speeds and velocities in jogging I. From ������ to ������ II. From ������ to ������? Q3. What is acceleration? How will you express it mathematically? Q4. When will you say a body is in (I) Uniform acceleration? (II) Non-uniform acceleration? Q5. A bus retards uniformly at a rate of 3 ������/������2 and stops in 10 ������. With what velocity was the bus travelling? Q6. In your everyday life you come across a range of motions in which I. Acceleration is in the direction of motion. II. Acceleration is against the direction of motion. III. Acceleration is uniform. IV. Acceleration is non-uniform. Can you identify one example each the above type of motion? Q7. A body moving with an initial velocity of 5 ������/������ accelerates at 2 ������/������2. Its velocity after 10 ������ is A) 20 ������/������ B) 25 ������/������ C) 5 ������/������ D) 22.5 ������/������ Q8. Give examples where I. The velocity is in opposite direction to the acceleration. II. The velocity of the particle is zero but its acceleration is not zero. III. The velocity is perpendicular to the acceleration. HOMEWORK Q1. An insect moves along a circular path of radius 10 ������������ with a constant speed. It takes 1 min to move from a point on the path to the diametrically opposite point. Find I. The distance covered. II. The speed. III. The displacement. IV. The average velocity. Q2. I. An object travels 30 ������ in 4 ������ and then another 30 ������ is 2 ������. What is the average speed of the object? II. Is the data given above sufficient to find average velocity of the object? III. Under what condition(s) is the magnitude of average velocity of an object equal to its average speed? 9P01.2

9P01 – Motion 5 Q3. State a relationship connecting ������������, ������������, ������������ and ������������ for an accelerated motion. Give an example of motion in which acceleration is uniform. Q4. What is meant by retardation or deceleration? Q5. The initial velocity of a train which is stopped in 20 ������������ by applying brakes (retardation due to brakes being 1.5 ������������/������������2) is A) 30 ������������/������������ B) 30 ������������������������/������������ C) 20 ������������������������/������������ D) 24 ������������/������������ Q6. A car increases its speed from 20 ������������������������/ℎ to 50 ������������������������/ℎ in 10 seconds. Its acceleration is A) 30 ������������/������������2 B) 3 ������������/������������2 C) 18 ������������/������������2 D) 0.83 ������������/������������2 Q7. A racer starts a car race from rest and finishes it with a velocity of 54 ������������������������/ℎ. Assuming constant acceleration of 3 ������������/������������2, Find the time it will take to finish the race. Q8. State the condition (s) under which the displacement of a particle and its average velocity are zero. What can be said about the corresponding average speed(s)? Q9. An object does not possess an acceleration or retardation when it moves A) In upward direction with decreasing speed B) In downward direction with increasing speed C) With constant speed along circular path D) With constant speed along a particular horizontal direction ADVANCED QUESTIONS Q1. A 50������������ ball travelling at 25 ������������/������������ bounces off a wall and rebounds at 24 m/s. A high speed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the magnitude of the average acceleration of the ball during this time interval? Q2. During a constant accelerated motion of a particle, average velocity of the particle A) is always less than its final velocity B) is always greater than its final velocity C) may be zero D) is half of its final velocity Q3. A police jeep is chasing a thief with a velocity of 72 ������������������������/ℎ. The thief is in another jeep with a velocity of 90 ������������������������/ℎ. The police fires a bullet with a velocity of 180 ������������/������������ (with respect to the jeep) when the thief is 350 metres away. Determine the time after which the bullet will hit the thief. 9P01.2

9P01 – Motion 6 9P01.3 Graphical Representation of Motion & Uniform Circular Motion CONCEPTS COVERED 1. Introduction of graph plotting – origin, axes, coordinates 2. Plotting motion on a graph 3. To find speed/velocity from a distance/displacement time graph 4. To find distance travelled using the area under the graph 5. To find acceleration from velocity time graph 6. Uniform circular motion and its various parameters IN CLASS EXERCISE Q1. What is the nature of distance time graphs for uniform and non-uniform motion of an object? Q2. From the ������-������ graph alongside, (see figure), what can be inferred? Q3. Make a velocity-time graph from the following displacement-time graph. Q4. How do we measure magnitude of displacement from a ������-������ curve? Q5. Find the displacement of a body whose velocity-time graph is shown alongside. Q6. The velocity-time graph (see figure below) shows the motion of a cyclist. Find: I. Its acceleration II. Its velocity after 15 ������ and III. The distance covered by the cyclist in 15 ������. Q7. A motorcyclist riding motorcycle ������ who is travelling at 36 ������������/ℎ applies the brakes and stops the motorcycle in 10 ������. Another motorcyclist of motorcycle ������ who is travelling at 18 ������������/ℎ applies the brakes and stops the motorcycle in 20 ������. Plot speed-time graph for the two motorcycles. Which of the two motorcycles travelled farther before it came to a stop? Q8. Can an object be accelerated if it is moving with constant speed? Justify your answer with an example. OR Can a body have constant speed and still be accelerating? Give an example. OR Explain how is it possible for an object to move with a constant speed but with uniform acceleration. 9P01.3

9P01 – Motion 7 HOMEWORK Q1. What do the graphs I) and II) shown here indicate? Q2. Find the total displacement of the body from the graph alongside. Q3. The driver of train ������ travelling at a speed of 54 ������������/ℎ applies brakes and retards the train uniformly. The train stops in 5 ������. Another train ������ is travelling on the parallel with a speed of 36 ������������/ℎ. Its driver applies the brakes and the train retards uniformly, train ������ stops in 10 ������. Plot speed-time graphs for both the trains. Which train travelled farther after the brakes were applied? Q4. The velocity-time graph for the motion of an object in a straight path is a straight line parallel to the time axis. I. Identify the nature of motion of the body. II. Find the acceleration of the body. III. Draw the shape of distance-time graph for this type of motion. Q5. Draw velocity-time graphs for the following cases: I. When the object is at rest. II. When the object is thrown vertically upwards. Q6. A particle is moving with uniform positive acceleration. Its velocity-time graph will be A) A straight line parallel to the time-axis B) A straight line inclined at an obtuse angle to the time-axis C) A straight line inclined at an acute angle to the time-axis D) None of the above Q7. Why is the motion of an athlete moving along the circular path, with a constant speed, an accelerated motion? Q8. An artificial satellite is moving in a circular orbit of radius 42250 ������������. Calculate its speed if it takes 24 hours to revolve around the earth. 9P01.3

9P01 – Motion 8 9P01.4 Equations of Motion CONCEPTS COVERED 1. Significance of velocity-time, position-time and position-speed relations 2. To find the equations of motion using graphical method 3. Solving various examples using the equations of motion IN CLASS EXERCISE Q1. State the three equations of motion. Which of them describes I. Velocity-time relation? II. Position-time relation? Q2. Deduce the following equations of motion. I. ������ = ������������ + (1) ������������2 II. ������2 = ������2 + 2������������ 2 Q3. Brakes applied to a car produce an acceleration of 6 ������/������2 in the direction opposite to motion. If the car takes 2 ������ to stop after the application of brakes, calculate the distance it travels during this time. Q4. A car starting from rest accelerates uniformly to acquire a speed 20������������/ℎ in 30 min. The distance travelled by car in this time interval will be: A) 600 ������������ B) 5 ������������ C) 6 ������������ D) 10 ������������ Q5. A trolley while going down an inclined plane has an acceleration of 2 ������������/������2. What will be its velocity 3 ������ after the start? Q6. A racing car starting from rest has a uniform acceleration of 4 ������/������2. What distance will it cover in 10 ������ after the start? Q7. A bus starting from rest moves with a uniform acceleration of 0.1 ������/������2 for 2 mins. Find I. The speed acquired II. The distance travelled. Q8. An electron moving with a velocity of 5 × 104������/������ enters into a uniform electric field and acquires a uniform acceleration of 104 ������/������2 in the direction of its initial motion. I. Calculate the time in which the electron would acquire a velocity double of its initial velocity. II. How much distance would the electron cover in this time? HOMEWORK Q1. An object starts linear motion with a velocity ‘������’ and under uniform acceleration ‘������’ it acquires a velocity ‘������’ in time ‘������’. Draw its velocity-time graph. From this graph obtain the following equations: I. ������ = ������ + ������������ II. ������ = ������������ + 1 ������������2 III. ������2 = ������2 + 2 ������������ 2 Q2. Velocity of a train changes from 20 ������/������ to 25 ������/������, when it accelerates at a rate 2 ������/������2. Find the distance covered by the train. Q3. A moving train is brought to rest within 20 ������ by applying brakes. If the retardation due to brakes is 2 ������/������2, then the initial velocity was A) 10 ������/������ B) 20 ������/������ C) 30 ������/������ D) 40 ������/������ Q4. A train is travelling at a speed of 90 ������������/ℎ������ . Brakes are applied so as to produce a uniform acceleration of −0.5 ������/������2. Find how far the train will go before it is brought to rest. Q5. A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3 ������/������2 for 8 ������. How far does the boat travel during this time? 9P01.4

9P01 – Motion 9 Q6. If the displacement of an object is proportional to square of time, predict the motion of the object. Q7. A stone is thrown in a vertically upward direction with a velocity of 5 ������/������. If the acceleration of the stone during its motion is 10 ������/������2 in the downward direction, what will be the height attained by the stone and what time will it take to reach there? Q8. A bullet initially moving with a velocity of 20������/������ strikes a target and comes to rest after penetrating a distance 10������������ in the target. Calculate the retardation caused by the target. Q9. Two stones are thrown vertically upwards simultaneously with their initial velocities ������1 and ������2, respectively. Prove that the heights reached by them would be in the ratio ������12: ������22. (Assume upward acceleration is −������ and downward acceleration is +������). ADVANCED QUESTIONS Q1. A particle having initial velocity ������ is moving with a constant acceleration ������ for a time ������. I. Find the displacement of the particle in the last 1 ������. II. Evaluate the displacement of particle in the last 1 ������ when ������ = 2 ������/������, ������ = 1 ������/������2 and ������ = 5 ������. Q2. A bullet of mass 0.006������������ travelling at 120������/������ penetrates deeply into a fixed target and is brought to rest in 0.01������. Calculate the distance of penetration in the target. Q3. A ball is tossed straight up from the ground. Half way up, it has a speed of 19.6������/������. Find I. Its initial velocity II. The maximum height reached Q4. A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance ������1 in the first 10 seconds and distance ������2 in the next 10 seconds, then A) ������2 = ������1 B) ������2 = 2������1 C) ������2 = 3������1 D) ������2 = 4������1 9P01.4

9P01 – Motion 10 Advanced Practice Problems Q1. The acceleration versus time graph of a particle moving along a straight line is shown in the figure. Draw the respective velocity – time graph. Given ������ = 0 at ������ = 0. Q2. Which of the following statements are true for a moving body? A) If its speed changes, its velocity must change and it must have some acceleration B) If its velocity changes, its speed must change and it must have some acceleration C) If it is accelerating, then its speed and velocity must change D) If its speed changes but direction of motion does not change, its velocity can remain constant Q3. The graph describes an airplane’s acceleration during its take – off run. The airplane’s velocity when it lifts off at ������ = 20������ is: A) 40������/������ B) 50������/������ C) 90������/������ D) 180������/������ Q4. The figure shows the velocity (������) of a particle plotted against time (������) Choose the correct alternative from the following. A) The particle changes its direction of motion at some point B) The acceleration of the particle remains constant C) The displacement of the particle is zero D) All of the above Q5. A ball moves on a smooth floor in a straight line with uniform velocity 10������/������ for 6������. At ������ = 6������, the ball hits a wall and comes back along the same line to the starting point with the same speed. Draw the velocity – time graph and use it to find the total distance travelled by the ball and its displacement. Q6. A particle starts with an initial velocity and passes successively over the two halves of a given distance with acceleration ������1 and ������2 respectively. Show that the final velocity is the same as if the whole distance is covered with a uniform acceleration (������1+������2) 2 Q7. A body moving along a straight line with uniform acceleration has a speed 15������/������ when passing a point ������ and 35������/������ when passing a point ������ in its path. Calculate its speed at the midpoint of ������������. Q8. A train, 100������ long and stationary, is given the all clear by a signal 80������ ahead of it. The train accelerates uniformly at 0.4������/������2. Find the time taken for the engine driver (at the front) and the guard (at the back) of the train to pass the signal. At what speed is the train moving at each of these times? A.P.P.

9P01 – Motion 11 Q9. The following figure represents the velocity – time graph of a particle moving in a straight line I. Did the particle ever move with uniform velocity? II. Did the particle ever move with uniform acceleration? III. What is the distance traversed by the particle in 4 seconds? If your answer to any of the parts I or II is yes, then specify the region(s) and also specify/ calculate the corresponding value(s) A.P.P.

12 Avanti 9P01 Motion CBSE Practice Problems

13 Avanti 9P01 Motion CBSE Practice Problems

14 Avanti 9P01 Motion CBSE Practice Problems

15 9P0 – –O

6. Read the given statements and select the correct option. 16 Statement 1 : For a given time interval, average velocity has single value while average speed can have many values. Statement 2 : Velocity is the speed of an object moving in a definite direction. A) Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1. B) Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1. C) Statement 1 is true but statement 2 is false. D) Both statements 1 and 2 are false. 7. A man in a lift ascending with an acceleration throws a ball vertically up with a velocity u and catches it after time t1• Afterwards when the lift is descending with the same acceleration, the man again throws a ball vertically up with the same velocity and catches it after time t2 • The velocity of projection of ball is A) nt1t, B) nt1t, C) nt1t2 D)�(2(t1+t2) (t1-t2) (t1+t2) 2(t,-t,) 8. A car accelerates from rest at a constant rate a for some time after which it decelerates at a constant rate /3 and comes to rest. If total time elapsed is t, then the maximum displacement of the car will be A) a+p B) (a,-p,)t2 C) -2acap+t-p2) D) Ca+p)t, apt2 ap ap 9. A rock is thrown downward from an unknown height above the ground with an initial speed of 10 m s-1. It strikes the ground 3.0 s later. Find the initial height of the rock above ground. A) 44m B) 14m C) 75m D) 30m 10. Match column I with column II and mark the correct option from the codes given below. Column - I Column - II P) Uniform velocity V L.I. a Q) Uniform acceleration h,II. R) Uniform retardation s L.III. s k_,S) Uniform acceleration with initial velocity IV. A) P - I, Q - II, R - III, S - IV B) P - II, Q - IV, R - III, S - I C) P - IV, Q - II, R - III, S - I D) P - III, Q - I, R - IV, S - II 11. On a straight road, a car starts from rest and accelerates at uniform rate of 6 m s-2 for some time, then moves with constant speed for some time and retards at the same uniform rate and comes to rest. Total time for the journey is 24 s and average speed for journey is 20 m s-1. How long does the car move with constant speed? A) 4s B) 8 s C) 12 s D) 16s 12. From a tower of height h a particle is thrown vertically upwards with a speed v. The time taken by the particle, to hit the ground is n times that taken by it to reach the highest point of its path. Then speed(u) of the particle is equal to jA)�gH B) ..Jzgii C) �..Jzgii D) ��� n 13. A car covers one-third of its journey with speed x, next one-third with speedy and the last one-third with speed z. The average speed of the body during the entire journey is A) 2xyz B) 3xyz C) xyz D) 3(x+y+z) xy+yz xy+yz xy+yz+xz xyz ------------ Avanti - 9P01 - Motion - Olympiad Practice Problems