Question

An object of mass 100kg is accelerated uniformly from a velocity of 5m/s to 8m/s in 6 seconds. Calculate the initial and final momentum of the object. Also find the magnitude of the force exerted on the object.

Answer 1

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Answer 2

$\bf{\underline{\underline{Answer:}}}$

$\bf{\therefore 50\:N}$

$\bf{\underline {Given:}}$

Initial velocity, $u \:=\:5\:{s}^{-1}$

Final velocity, $v \:=\:8\:{s}^{-1}$

Mass of the given object, $m = 100\:kg$

Time, $t\:=\:6\:s$

$\bf{\underline {To\:Find:}}$

Initial momentum and final momentum =?

Magnitude of force exerted on the object =?

We know that,

Momentum, p = Mass × Velocity

Therefore, initial momentum,

= Mass × Initial velocity

${100×5=500\:kg \:m\:{s}^{-1}}$

Final momentum,

= Mass × Final velocity

${100×8=800\:kg\:m\:{s}^{-1}}$

$<b>To find the magnitude of the force exerted on the object :</b>$

We know that,

$v \:= \:u \:+ \:at$

$8 \:= \:5 \:+ \:a\:×\:6$

$8 \:-\:5 \:= \:a\:×\:6$

$a =\dfrac{3}{6}\:=\:0.5\:m\:{s}^{-2}$

Now, force exerted on object

= Mass × Accleration

= 109 × 0.5

$= \bf{50\:N}$