Question

an object of a mass 100 kg is accelerated uniformly from a velocity of 5 m/s to 8 m/s in 6 seconds.Calculate the magnitude of the force,exerted on the object
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Answer 1

${\huge{\underline{\blue{Given:}}}}$

mass m = 100 kg

initial velocity u = 5 m/s

final velocity v = 8 m/s

time t = 6 sec

${\huge{\underline{\pink{To \: Find:}}}}$

Magnitude of force

${\huge{\underline{\orange{Formula:}}}}$

v = u + at ; F = ma

${\huge{\underline{\green{Solution:}}}}$

v = u + at

8 = 5 + a(6)

a = 3/6 = 1/2 m/s²

__________________________

F = ma

F = 100 × 1/2

F = 50N

${\underline{\red{Answer: \: 50N}}}$

Answer 2

To Find :

The Rate of change of Momentum.

Given :

• Mass of the Body = 100 kg

• Initial Velocity = 5 m/s

• Final velocity = 8 m/s

• Time Taken = 6 s

We Know :

MaGnitude of Force :

$\implies \bf{\boxed{Rate\:of\:Momentum = \dfrac{\overrightarrow{p_{2}} - \overrightarrow{p_{1}}}{\Delta t}}}$

Where,

• $\bf{p_{1}$ = Initial Momentum

• $\bf{p_{2}$ = Final Momentum

• ∆ t = Change in time .

Solution :

• m = 100 kg

• u = 5 m/s

• v = 8 m/s

• t = 6 s

Using the formula and substituting the values in it , we get :

$\bf{\boxed{Rate\:of\:Momentum = \dfrac{\overrightarrow{p_{2}} - \overrightarrow{p_{1}}}{\Delta t}}} \\ \\ \\ \implies \bf{Rate\:of\:Momentum = \dfrac{m\overrightarrow{v} - m\overrightarrow{u}}{\Delta t}} \\ \\ \\ \implies \bf{Rate\:of\:Momentum = \dfrac{m(v - u)}{t}} \\ \\ \\ \implies \bf{Rate\:of\:Momentum = \dfrac{100 \times (8 - 5)}{6}} \\ \\ \\ \implies \bf{Rate\:of\:Momentum = \dfrac{100 \times 3}{6}} \\ \\ \\ \implies \bf{Rate\:of\:Momentum = \dfrac{100 \times \not{3}}{\not{6}}} \\ \\ \\ \implies \bf{Rate\:of\:Momentum = \dfrac{100}{2}} \\ \\ \\ \implies \bf{Rate\:of\:Momentum = 50 N} \\ \\ \\ \therefore \purple{\bf{Rate\:of\:Momentum = 50 N}}$

Hence, the magnitude of the force is 50 N.