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Velocity and acceleration of a particle ...

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

Text Solution

Verified by Experts

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.
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