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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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The correct Answer is:
A
Here, acceleration `a=(4 hati+3 hatj) m//s^2` is constant.
So, we can apply
`v=u+at`
and `s=ut+1/2at^2`
Substituting the proper values, we get
`v=(2 hati+3 hatj)+(2)(4 hati+3hatj)`
`=(10 hati+9hatj) m//s`
and `s=(2)(2 hati+3 hatj)+1/2(2)^2(4 hati+3 hatj)`
`=(12 hati+12 hatj)m`
Therefore, velocity and displacement of particle at `t=2s are (10 hati+9 hatj) m//s and (12 hati+12 hatj)m`
respectively.
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Knowledge Check

  • 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.

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    `(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`

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    B
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