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An object of mass $100 \mathrm{~kg}$ is accelerated uniformly from a velocity of $5 \mathrm{~m} \mathrm{~s}^{-1}$ to $8 \mathrm{~m} \mathrm{~s}^{-1}$ in $6 \mathrm{~s}$. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object

Solution

Here, $m=100 \mathrm{~kg}$

$u=5 \mathrm{~m} \mathrm{~s}^{-1}$

$v=8 \mathrm{~m} \mathrm{~s}^{-1}, t=6 \mathrm{~s}$

Initial momentum of object, $p_{1}=m u$ $=100 \times 5=500 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$

Final momentum of object, $p_{2}=m v$ $=100 \times 8=800 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$

Force $=(800-500) / 6=50 \mathrm{~N}$

So,the Force is 50 N

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