The acceleration-time graph of a particle moving along x-axis is shown in the figure. If the particle starts with velocity 3 m/s at t = 0, find the velocity of particle at t = 4 s.

Explanation

The velocity at t = 4 s will depend on the change in velocity of the particle in the interval 0 to 4 s which is given by the area under a-t graph. Before calculating area let us find the acceleration at t = 4 s.
`tantheta=(8-a_(0))/(4)=(8)/(8)" (by the graph)"`
`rArr" "a_(0)=4m//s^(2)`
`"Change in velocity "="Area between 0 to 4 s"`
`=(1)/(2)xx(4+8)xx4=24m//s`
`rArr" final velocity (v)"-"initial velocity (u) = 24"`
`rArr" "v=u+24=3+24=27m//s`