Accleration vs time graph of a particle starting from rest is given. Find the displacement of particle in first 2 seconds.

Options

A. `(3)/(8)`
B. `(8)/(3)`
C. `(4)/(3)`
D. `(3)/(16)`

Answer

B

Explanation

for `0 le t lt 2` sec acceleration is `a = 2 - t`
`underset(0)overset(v)(int) dv = underset(0)overset(t)(int) (2 - t) dt`
`v = 2t (t^(2))/(2)`
`underset(0)overset(x_(1))(int)(2t - (t^(2))/(2)) dt rArr x_(1) = (8)/(3) m`