# Motion

## Revision Notes

• Rest : When a body does not change its position with respect to time and its surroundings, the body is said to be at rest.
• Motion : When a body continuously changes its position with respect to time and its surroundings, the body is said to be in motion.
• Locomotion : The motion performed by living beings (animals and plants) is called locomotion.
• Characteristics (properties) of a moving body :
• There must be a reference point (a stationary object) to describe the position of a given body.
• The position of the given body must continuously change with time and with respect to reference point.
• Distance : It is the actual length of the path travelled by a moving body, irrespective of the direction of motion of the body.
• Displacement : The shortest distance of a moving body from the point of reference (initial position of the body) in a specifed direction is called displacement.
• Uniform motion : When a body covers equal distances in equal intervals of time, however small may be time intervals, the body is said to describe uniform motion.
• Non-uniform motion : When a body covers unequal distances in equal intervals of time, it is said to be moving with non-uniform motion.
• Speed : The rate of change of motion is called the speed.
• Mathematical expression for speed :
Speed = Distance ÷ Time.
SI unit of speed is metre per second (ms–1 or m/s).
• Uniform speed : When a body covers equal distances in equal intervals of time, however small may be the time intervals, the body is said to be moving with uniform speed.
• Variable speed : When a body covers unequal distances in equal intervals of time, the body is said to be moving with variable speed.
• Average speed : The average distance covered by a body per unit time, when the body is moving with a variable speed is called average speed.
• Velocity : The distance covered by a body per unit time in a specifed direction is called velocity. It is vector quantity and has same units as speed.
• Uniform velocity : When a body covers equal distances in equal intervals of time (however small may be the time intervals) in a specifed direction, the body is said to be moving with uniform velocity.
• Variable velocity or Non-uniform velocity : When a body covers unequal distances in equal intervals of time in a specifed direction or when a body covers equal distances in equal intervals of time, but its direction changes, then the body is said to be moving with a variable velocity.
• Acceleration : The rate of change of velocity of a moving body is called acceleration. It is vector quantity and its unit is metre per square second (ms–2 or m/s2).
• Positive acceleration : The rate of change of velocity of a moving body, when the velocity is increasing is called positive acceleration.
• Negative acceleration : The rate of change of velocity of a moving body, when the velocity is decreasing is called negative acceleration or retardation.
• Conclusions from a distance-time graph.
• If the graph is parallel to the time axis, then the body is stationary.
• If the graph is a straight line, but not parallel to time axis then the body is moving with a uniform speed.
• If the graph is a curve, it implies that body is moving with a variable speed and has accelerated motion.
• Conclusions from a velocity-time graph.
• When the velocity-time graph is a straight line parallel to time axis.
The body is moving with a uniform velocity and its acceleration is zero.
The displacement of body can be calculated from the area under graph line.
• When the velocity-time graph is a straight line, but not parallel to time axis.
The body is moving with a variable velocity, but uniform acceleration.
The uniform acceleration/deceleration can be calculated by finding slope of the graph. If the slope is positive then it is positive acceleration. If slope is negative then it is retardation
The displacement of a body can be calculated by finding area under the velocity-time graph line.
• If a body having initial velocity ‘u’ is acted upon an acceleration ‘a’ for the time ‘t’ such that ‘v’ is its final velocity and s is distance covered then :
• v = u + at
• s = ut + ½ at2
• v2 = u2 + 2as
• Uniform circular motion : When a body moves in a circular path with uniform motion.

# Important Questions

1. Prove that v = u + at, using graphical method.
2. Derive the equation s = ut +½ at2 using graphical method.
Or,
Draw a graph velocity versus time for a body starts to move with velocity 'u' under a constant acceleration a for time t. Using this graph derive an expression for distance covered 's' in time 't'.
3. Derive the equation v2 – u2 = 2as graphically.
4. How can you calculate the following :
(a) Speed from distance-time graph.
(b) Acceleration from velocity-time graph.
(c) Displacement from velocity-time graph.
5. Draw the distance-time graph for the following situations :
(a) When a body is stationary.
(b) When a body is moving with a uniform speed.
(c) When a body is moving with variable speed and uniform acceleration.
6. Draw velocity-time graphs for the following situations :
(a) When the body is moving with uniform velocity.
(b) When the body is moving with variable velocity and uniform acceleration.
(c) When the body is moving with variable velocity and uniform deceleration.
7. What can you conclude about the motion of a body depicted by the velocity-time graphs (i), (ii) and (iii) given below :
8. Look at the figure below :

An object starts its journey from point 0. A, B, C, D and E represent position of the object at different instants. The object moves through A, B, C, D and E and then moves back to point C.
Calculate :
(a) the distance travelled by the object
(b) the displacement of the object
(c) name the reference point in the diagram.
9. A car is running at a speed of 54 km h–1. In the next second, its speed is 63 km h–1. Calculate the distance covered by the car in metre.
10. The length of minute hand of a clock is 14 cm. Calculate the speed with which the tip of the minute hand moves.
11. While driving Jayant travels 30 km with a speed of 40 km/h and next 30 km with a uniform speed of 20 km/h. Find his average speed.
12. An object travels 16 m in 4 seconds and the next 16 m in 2 seconds. Calculate the average speed of the object.
13. A bus travels at a distance of 120 km with a speed of 40 km/h and returns with a speed of 30 km/h. Calculate the average speed for the entire journey.
14. A motorcyclist drives from A to B with a uniform speed of 30 km h–1 and returns back with a speed of 20 km h–1. Find its average speed.
15. Ali while driving to school, computes the average speed for his trip to be 20 km/h. On his return trip along the same route there is less traffc and the average speed is 30 km/ h. What is the average speed for Ali's trip?
16. Rajeev went from Delhi to Chandigarh on his motorbike. The odometer of the bike read 4200 km at the start of trip and 4460 km at the end of his trip. If Rajeev took 4 h 20 minutes to complete his trip, fnd the average speed in kmh–1 as well as ms–1.
17. Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 50 seconds and then turns around and jogs 100 m back of point C in another 1 minute. What are Joseph's average speeds and velocities in jogging?
(a) from A to B and
(b) from A to C?
18. A bus accelerates uniformly from 54 km/h to 72 km/h in 10 s. Calculate : (i) the acceleration (ii) the distance covered by the bus in that time.
19. A car starts from rest and moves along the x-axis with a constant acceleration of 5 m s–2 for 8 seconds. If it then continues to move with a constant velocity, what distance will the car cover in 12 seconds since it started from rest?
20. The velocity-time graph shows the motion of a cyclist. Find (i) its acceleration (ii) its velocity and (iii) the distance covered by the cyclist in 15 seconds.
21. A train starting from rest attains a velocity of 72 km/h in 5 minutes. Assuming the acceleration is uniform. Find
(i) the acceleration
(ii) the distance travelled by the train for attaining this velocity.
22. A girl walks along a straight path to drop a letter in the letter box and comes back to her initial position. Her displacement-time graph is shown in the fgure. Plot a velocity-time graph for the same.
23. An object is dropped from rest at a height of 150 m and simultaneously another object is dropped from rest at a height 100 m. What is the difference in their heights after 2 s if both the objects drop with same acceleration? How does the difference in heights vary with time?
24. Starting from a stationary position , Rehan paddles his bicycle to attain a velocity of 6 m/s in 30 s. Then he applies brakes such that the velocity of the bicycle comes down to 4 m/s in the next 5 s. Calculate the acceleration of the bicycle in both the cases.
25. The brakes applied to a car produce an acceleration of 6 m/s2 in the opposite direction to the motion. If the car takes two seconds to stop after the application of brakes, calculate the distance it travels during this time.
26. The driver of a train A travelling at a speed of 54 km/h applies brakes and retards the train uniformly. The train stops in 5 s. Another train B is travelling on the parallel track with a speed of 36 km/h. This driver also applies the brakes and the train retards uniformly. The train B stops in 10 s. Plot speed - time graph for both the trains on the same paper. Also calculate the distance travelled by each train after the brakes were applied.
27. An object starting from rest travels 20 m in the first 2 s and 160 m in the next 4 s. What will be the velocity after 7 s from the start?
28. The velocity-time graph of a car is given below.

The car weighs 1000 kg.
(i) What is the distance travelled by the car in the frst 2 seconds?
(ii) What is the braking force at the end of 5 seconds to bring the car to a stop within one second?
29. A train starting from rest, picks up a speed of 20 ms–1 in 200 s. It continues to move at the same speed for the next 500 s. It is then brought to rest in the next 100 s.
1. Plot a speed time graph.
2. Calculate the rate of uniform acceleration.
3. Calculate the rate of uniform retardation.
4. Calculate the distance covered by the train during retardation.
5. Calculate the average speed during retardation.
30. Two stones are thrown vertically upwards simultaneously with their initial velocities u1 and u2 respectively. Prove that the heights reached by them would be in the ratio of u12 : u22 (Assume upward acceleration to be –g and downward acceleration to be +g).
31. An electron moving with a velocity of 5 × 104 ms–1 enters into a uniform electric field and acquires a uniform acceleration of 104 ms–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) What distance would the electron cover in this time?
32. Using the following data, draw time-displacement graph for a moving object :

Use this graph to fnd average velocity for the first 4 s, for the next 4 s and for the last 6 s.
33. Look at the figure below:
(a) Name the kind of motion of the stone.
(b) Is this an example of accelerated motion? Why?
(c) Name the force that keeps the stone in its path.
(d) What is the direction of this force? Draw it in your answer sheet.
34. Suggest real life examples where the motion of a body is similar to that represented by the following velocity-time graphs:
35. The V-T graph of cars A and B which start from the same place and move along a straight road in the same direction, is shown. Calculate
(i) the acceleration of car A between 0 and 8 s.
(ii) the acceleration of car B between 2 s and 4 s.
(iii) the points of time at which both the cars have the same velocity
(iv) which of the two cars is ahead after 8 sec. and by how much?