Important questions based on NCERT syllabus for Chapter 3 - Motion in a Straight Line:
Question-1: Why is there no distinction required between instantaneous speed and magnitude of velocity?
Solution: Instantaneous velocity is the first derivative of distance with respect to time (dx / dt). However, dt is so small it is assumed that the moving particle does not change direction. As a result the total distance and the magnitude of displacement becomes equal in this time interval. Thus, instantaneous speed and magnitude of velocity is equal.
Question-2: The figure given below is a x-t plot of an object’s motion in one dimensional. On the figure three different equal time intervals are marked. Find the intervals in which the average speed is the least and the greatest. Also write the sign of average velocity at each interval.
Solution: The slope of the graph is minimum at 2 and maximum at 3. Thus, the least average speed is at time interval 2 and the greatest average speed is at time interval 3. Average velocity is positive in interval 1 and 2, and negative in 3.
Question-3: A lady stands in an elevator which is open from above. She then throws a ball up with an initial speed of 40 m/s. After how long will the ball return to her hand? The elevator then starts moving upwards with a uniform speed of 5 m s-1 , the lady again throws the ball up with the same initial speed, after how long will the ball return to her hand?
Case 1 when the elevator is still:
v = u + at
0 = 40 + (- 9.8 )t (Since final velocity = 0 and a = -g as gravity acts downwards)
-40/-9.8 = t
= 4.081 s.
Thus, the total time taken by the ball to go up and return back is 4.081 x 2 =8.16 s
Case 2 when the elevator is moving upwards :
The elevator moves up at a constant speed thus the relative velocity of the ball with respect to the lady remains the same. Thus it takes 8.16 s for the ball to go up and down.