The net force acting on a particle moving along a straight line varies with time as shown in the diagram. Force is parallel to velocity. Which of the following graph is best representative of its speed with time? (Initial velocity of the particle is zero)

Options

A. (a)
B. (b)
C. (c)
D. (d)

Answer

A

Explanation

`a=F/m` or `apropF`

Hence, `a-t` graph is similar to `F-t` graph.
From O to `t_1`
`apropt`
or `a=kt` (`krarra` positive constant)
Integrating we get,
`v=(kt^2)/(2)` or `vpropt^2`
i.e. `v-t` graph is a parabola passing through origin.
From `t_1` to `t_2` again acceleration is positive (in the direction of velocity). So, velocity will further increase.