The graph below shows the distance traveled by a ball when moving on a straight

Question

The graph below shows the distance traveled by a ball when moving on a straight line, as a function of time. The ball motion starts at time 0 s where the distance is 0 m. Match the letters on the graph with the corresponding statements about the motion.

Time interval when the velocity and acceleration are non zero. A B C D E

Time interval when the velocity and the acceleration are both zero. A B C D E

Time interval when the magnitude of the velocity is the highest. A B C D E

Time interval when the ball is moving forward at constant speed. A B C D E

Time interval when the magnitude of the acceleration is the largest A B C D E

Explanation / Answer

veloicty=slope of distance vs time curve

acceleration=second derivative of distance vs time curve

part 1:

Time interval when the velocity and acceleration are non zero:

will be when the distance vs time curve is parabolic in nature so that both first and second derivative will be non zero

this time interval is A.

part 2:
Time interval when the velocity and the acceleration are both zero

when distance vs time curve is constant so that all the derivatives are zero

hence time C

part 3:

magnitude of velocity=slope of distance vs time curve

hence magnitude will be highest when slope is highest

which is time interval B

part 4:

constant speed means a straigh line curve for distance vs time curve so that derivative will be constant

hence time interval B

part 5:

magnitude of acceleration means second derivative of the curvee

so time interval A is the correct option

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