Question

when a force is applied on a body of mass 10kg for a period of 4 s‚ the velocity of the body changes from 6m/s to 8m/s​

Answer 1

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⋆ This question says that we have to find out the force that is applied on a body that have mass 10 kilograms. The force is applied on the body for a period of 4 seconds. Afterthat the velocity of the body changes from 6 metre per second to 8 metre per second.

${\bigstar \:{\pmb{\sf{\underline{Provided \: that...}}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀When a force is applied on a body of mass 10 kg for a period of 4 second‚ the velocity of the body changes from 6m/s to 8m/s.

$\sf According \: to \: statement \begin{cases} & \sf{Initial \: velocity \: = \bf{6 \: m/s}} \\ \\ & \sf{Final \: velocity \: = \bf{8 \: m/s}} \\ \\ & \sf{Mass \: of \: body \: = \bf{10 \: kg}} \\ \\ & \sf{Time \: = \bf{4 \: seconds}} \\ \\ & \sf{Force \: = \bf{?}} \end{cases}$

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⋆ Acceleration: The term acceleration is a measure of the change in the velocity of an object per unit time.

${\small{\underline{\boxed{\sf{Acceleration \: = \dfrac{Change \: in \: velocity}{Time \: taken}}}}}}$

If the velocity of an object is changes from initial value u to the final value v in the time t the acceleration a be

⠀⠀⠀⠀⠀${\small{\underline{\boxed{\sf{a \: = \dfrac{v-u}{t}}}}}}$

The SI unit of acceleration is m/s²

☯ As in the question it is provided that we have to find out the force applied on body according to the condition. Then why we are using acceleration formula?

➣ Firstly the force is given by that is the formula to find the force is

${\small{\underline{\boxed{\sf{Force \: = Mass \times Acceleration}}}}}$

Force f is the product of mass m and acceleration a -

⠀⠀⠀⠀⠀${\small{\underline{\boxed{\sf{f \: = ma}}}}}$

That's the reason here we have to use acceleration formula as we haven't value of a while using formula of force.

${\bigstar \:{\pmb{\sf{\underline{Full \: Solution...}}}}}$

~ Firstly let us find acceleration by using the formula to find acceleration!

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time \: taken} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{8-6}{4} \\ \\ :\implies \sf a \: = \dfrac{2}{4} \\ \\ :\implies \sf a \: = \cancel{\dfrac{2}{4}} \quad \quad (Cancelling) \\ \\ :\implies \sf a \: = \dfrac{1}{2} \\ \\ :\implies \sf Acceleration \: = \dfrac{1}{2} \: m/s^{2}$

~ Now as we get the acceleration so let us use formula to find force and let's solve this whole question!

$:\implies \sf Force \: = Mass \times Acceleration \\ \\ :\implies \sf f \: = ma \\ \\ :\implies \sf f \: = m \times a \\ \\ :\implies \sf f \: = 10 \times \dfrac{1}{2} \\ \\ :\implies \sf f \: = \cancel{10} \times \dfrac{1}{\cancel{{2}}} \quad \quad (Cancelling) \\ \\ :\implies \sf f \: = 5 \times 1 \\ \\ :\implies \sf f \: = 5 \\ \\ :\implies \sf Force \: = 5 \: Newton$