The acceleration of a particle varies with time as shown in .
.
a. Find an expression for velocityinterms of `t`. Assume that `v=0` at `t=0`
b. Calculate the displacement of the paarticle in the time interval from `t=2s` s.

Answer

`a=2t-2`
`a=t^(2)-2t`;
`(20)/(3)m`

Explanation

`a=2t-2`
a. `int_(0)^(v) dv=int_(0)^(t) a dt rArr v=(2t^(2)//2t)_(0)^(t) =t^(2) -2t`
b. ` S=int_(2)^(4) v dt=(t^(3)/(3)-2(t^(2))/(2))_(2)^(4)=(20)/(3)m`.