Question

For a particle moving in a straight line, the velocity-time graph is as shown in the figure. Find the acceleration at time `t=1 s 2.5 s` and `5 s`. Sketch the acceleration time graph.

Answer 1

As the slope of the s-t graph gives the velocity, in the same manner, the slope of the v-t graph gives the acceleration.
`O` to `A: Slope=10/2=5`
`a=5 m//s^(2)` for `t=0` to `2 s`
`A` to `B`: Slope=0
`a=0` for `t=2` to `3 s`
`B` to `C: Slope=-10/5=-2`
`a=-2 m//s^(2)` for `t=3` to `8 s`
At `t=1 s, a=5 m//s^(2)`
`t=2.5 s, a=0`
`t=5 s, a=-2 m//s^(2)`
Acceleration-time `(a-t)` graph