Velocity and acceleration of a particle at time t=0 are `vecu =(2hati + 3hatj)m//s` s and `a = (4hati +2hatj) m//s^(2)` respectively. Find the velocity and displacement of particle at t = 2s.

Explanation

Here, acceleration
`vec(a) = (4hat(i) + 2hat(j))m//s^(2)` is contant.
So, we can apply `vec(v) = vec(u) + vec(a)t` and `vec(s) = vec(u) t + (1)/(2) vec(a) t^(2)` substituting the proper values, we get
`vec(v) = (2hat(i) + 3hat(j)) + (2)(4hat(I) + 2hat(J)) = (10hat(I) + 7hat(J))m//s`
and `vec(s) = (2)(2hat(i) + 3hat(j)) + (1)/(2)(2)^(2)(4hat(I) + 2hat(J)) = (12 hat(I) + 10hat(J))m//s`
Therefore, velocity and displacement of particle at t = 2s are `(10 hat(i) + 7hat(j))m//s` and `(12hat(i) + 10 hat(j))m` respectively.