Class 11 Physics

Motion in Straight Line

NCERT Solution

Part 4

Question 17: The following figure shows x-t plot of one-dimensional motion of a particle. Is it correct to say from the graph that the particle moves in a straight line for t < 0 and on a parabolic path for t > 0? If not, suggest a suitable physical context for this graph.

distance-time graph

Answer: x-t graph cannot show trajectory of particle, so it is incorrect to say that the particle moves in a straight line for t < 0 and on a parabolic path for t > 0. A suitable context for this graph is when an object is thrown from a height and then x = 0 when t = 0.

Question 18: A police van moving on a highway with a speed of 30 km h-1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km h-1. If the muzzle speed of the bullet is 150 m s-1, with what speed does the bullet hit the thief’s car?

Answer: Speed of police van = 30 km/h `=30xx5/(18)=(25)/3` m/s

Speed of thief = 192 km/h `=192xx5/(18)=(160)/3` m/s

Speed of bullet when it is fired `=(25)/3+150=(475)/3` m/s

Relative speed of bullet wrt thief `=(475)/3-(160)/3=(315)/3=105` m/s

Question 19: Suggest a suitable physical situation for each of the following graphs.

distance-time graph velocity-time graph acceleration-time graph

Answer:

  1. This is x-t graph. Let us imagine a situation when a player kicks a ball. The speed of ball increases from zero to a certain value and then the ball hits an obstacle (a wall or another player). The ball rebounds with reduced speed and gradually comes to a stop behind the first player.
  2. This shows v-t graph. A ball is dropped on ground, bounces back with reduced speed. The ball is bouncing repeatedly and finally comes to rest.
  3. This is a-t graph. A car is moving with uniform speed and then it accelerates for some time. After that, the car once again moves with uniform speed.

Question 20: The given figure gives x-t plot of a particle executing one-dimensional simple harmonic motion. Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, -1.2 s.

distance-time graph

Answer: (a) at 0.3 s position negative, velocity negative and acceleration positive, (b) at 1.2 s position positive, velocity positive and acceleration negative, (c) at -1.2 s position negative, velocity positive and acceleration positive

Question 21: The following figure gives the x-t plot of a particle in one-dimensional motion. Three different equal intervals of time are shown. In which interval is the average speed greatest, and in which is it the least? Give the sign of average velocity for each interval.

distance-time graph

Answer: Maximum at t = 3 and least at t= 2, v > 0 at 1 and 2, while v < 0 at 3

Question 22: The following figure gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion, give the signs of v and a in the three intervals. What are the accelerations at the points A, B, C and D?

speed-time graph

Answer: Acceleration is greatest in interval 2

Average speed is greatest in interval 3 which is evident from the highest peak in this interval

In all the three intervals v > 0

Acceleration at points A, B, C and D = 0