Question

A particle is moving along x-axis and its position time graph is given below. What could be the possible velocity-time and acceleration-time graph? (All the curves in the graph are parabolic. Only the part between $t_1$ and $t_2$ is straight line.)

• A.
• B.
• C.
• D.

Answer 1

Answer: (A), (C)

The correct options are
A
C

Conceptual

For parabola, $x=k{t}^2\Rightarrow V=2kt$ and $a=2k$
For straight line, $x=kt\Rightarrow V=k$ and $a=0$

In $0<t<t_1$, slope is increasing, so acceleration is +ve, velocity is increasing.
In $t_1<t<t_2$, slope is constant, so acceleration is 0, velocity remains constant.
In $t_2<t<t_4$, slope is decreasing, so acceleration is -ve, velocity is decreasing.
In $t_4<t<t_5$, slope is increasing, so acceleration is +ve and velocity is increasing.