Question

A body of mass 1kg is kept at rest. A constant force of 6.0 N starts acting on it. Find the time taken by the body to move through a distance of 12m.
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Answer 1

Given :-

Mass of the body = 1 kg

Force of the body = 6 N

Distance covered by the body = 12 m

To Find :-

The time taken by the body.

Analysis :-

Here we are given with the distance, force and mass of the body.

Firstly find the acceleration by substituting the given values such that force is equal to mass multiplied by acceleration.

Using the second equation of motion, find the time taken accordingly.

Solution :-

We know that,

• f = Force
• u = Initial velocity
• a = Acceleration
• m = Mass
• s = Distance

Using the formula,

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

Given that,

Force (f) = 6 N

Mass (m) = 1 kg

Substituting their values,

⇒ f = ma

⇒ 6 = 1 × a

⇒ a = f/m

⇒ a = 6/1

⇒ a = 6 m/s

Using the formula,

$\underline{\boxed{\sf Second \ equation \ of \ motion=s=ut+\dfrac{1}{2} at^2}}$

Given that,

Distance (s) = 12 m

Acceleration (a) = 6 m/s

Initial velocity (u) = 0 m/s

Substituting their values,

⇒ 12 = 0 × t + 1/2 × 6 × t²

⇒ 12 = 0 + 3t²

⇒ t² = 12/3

⇒ t² = 4

⇒ t = √4

⇒ t = 2 sec

Therefore, the time taken by the body to move is 2 sec.