Question

A force acts for 0.1 second on a body of mass 2.0 kg initially at rest. the force is then withdrawn and the body moves with a velocity of 2 metre per second. find the magnitude of force. ​

Answer 1

Given :-

Time taken by the body = 0.1 sec

Mass of the body = 2 kg

Initial velocity of the body = 2 m/s

To Find :-

The magnitude of the force.

Analysis :-

Here we are given with the time taken, mass, initial velocity and the final velocity of the body.

Using the first equation of motion, you can easily substitute the given values and find the acceleration accordingly.

Then substitute the values you got such that force is equal to mass multiplied by acceleration and find the force.

Solution :-

We know that,

• u = Initial velocity
• a = Acceleration
• m = Mass
• v = Final velocity
• f = Force

Using the formula,

$\underline{\boxed{\sf First \ equation \ of \ motion=v=u+at}}$

Given that,

Time (t) = 0.1 sec

Initial velocity (u) = 0 m/s

Final velocity (v) = 2 m/s

Substituting their values,

⇒ 2 = 0 + (a) 0.1

⇒ a = (v-u) / t

⇒ a = (2-0) / 0.1

⇒ a = 2/0.1

⇒ a = 20 m/s

Using the formula,

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

Given that,

Mass (m) = 2 kg

Acceleration (a) = 20 m/s

Substituting their values,

⇒ f = ma

⇒ f = 2 × 20

⇒ f = 40 N

Therefore, the magnitude of force is 40 N.

Answer 2

Given :-

• Time taken by the body = 0.1 sec

• Mass of the body = 2 kg

• Initial velocity of the body = 2 m/s

To Find :-

• The magnitude of the force.

Analysis :-

Here we are given with the time taken, mass, initial velocity and the final velocity of the body.

Using the first equation of motion, you can easily substitute the given values and find the acceleration accordingly.

Then substitute the values you got such that force is equal to mass multiplied by acceleration and find the force.

Solution :-

We know that,

• u = Initial velocity
• a = Acceleration
• m = Mass
• v = Final velocity
• f = Force
• Using the formula,

$\underline{\boxed{\sf First \ equation \ of \ motion=v=u+at}}$

Given that,

• Mass (m) = 2 kg

• Acceleration (a) = 20 m/s

Substituting their values,

⇒ 2 = 0 + (a) 0.1

⇒ a = (v-u) / t

⇒ a = (2-0) / 0.1

⇒ a = 2/0.1

⇒ a = 20 m/s

Using the formula,

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

Given that,

• Mass (m) = 2 kg

• Acceleration (a) = 20 m/s

Substituting their values,

⇒ f = ma

⇒ f = 2 × 20

⇒ f = 40 N

Therefore, the magnitude of force is 40 N.