Question

A body is at rest,what force will you apply to the body to move it through a distance of 12m in 4s.mass of the body is 3kg​

Answer 1

Answer :

• 4.5 N

Given Information :

• Initial velocity (u) = 0 [Since , it is at rest.]

• Distance (s) = 12 m

• Time (t) = 4 s

• Mass of the body (m) = 3 kg

To calculate :

• Force needed to apply to move it through a distance of 12m in 4s.

Calculation :

We know that,

★ F = ma

• F denotes force
• m denotes mass
• a denotes acceleration

In order to calculate force applied, we need to find acceleration first.

By using the second equation of motion,

$\boxed{\sf {s = ut + \dfrac{1}{2} at^2 }}$

• s denotes distance
• u denotes initial velocity
• t denotes time

$\longmapsto \sf {12 = ( 0 \times 4 ) + \dfrac{1}{2} \times a \times (4)^2 }$

$\longmapsto \sf {12 = \dfrac{1}{2} \times a \times 16 }$

$\longmapsto \sf {12 = 1 \times a \times 8 }$

$\longmapsto \sf {12 =8a }$

$\longmapsto \sf {\dfrac{12}{8} =a }$

$\longmapsto \sf {\dfrac{3}{2} =a }$

$\longmapsto \sf { 1.5 =a }$

$\longmapsto \boxed{ \sf { Acceleration = 1.5 m \: s^{-2} }}$

Now, as we know that :

$\boxed{\sf {F = ma}}$

By substituting values, we get :

$\longmapsto \sf { F = ( 3 \times 1.5) N }$

$\longmapsto \sf \red { F = 4.5 \: N }$

Therefore, 4.5 N of force is needed move it through a distance of 12m in 4s.