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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

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Here, accelration `veca=(4hat(i)+2hat(j))"m/s"^(2)` is constant.
So, we can apply `vecv=vecu+vecat` and `vecs = vecut+(1)/(2)vecat^(2)`
Substituting the proper values, we get
`vecv=(2hat(i)+3hat(j))+(2)(4hat(I)+2hat(J))=(10hat(I)+7hat(J))`m/s and
`vecs=(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.
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