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

Options

A. `(10hat(i)+7hat(j))m//s` and `(12hat(i)+10hat(j))m`
B. `(10hat(i)+2hat(j))m//s` and `(12hat(i)+10hat(j))m`
C. `(10hat(i)+7hat(j))m//s` and `(12hat(i)+1hat(j))m`
D. `(1hat(i)+7hat(j))m//s` and `(12hat(i)+10hat(j))m`

Answer

D

Explanation

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