Question

A body of mass 2 kg is moving with a velocity 8 m/s on a smooth surface. If it is to be brought to rest in 2 seconds, then the force to be applied is
(a) 8N
(b) 4 N
(c) 2 N
(d) 1 N
​

Answer 1

Given

A body of mass 2 kg is moving with a velocity 8 m/s on a smooth surface. It is brought to rest in 2 seconds.

So

m = 20 kg

u = 8 m/s

v = 0 m/s

t = 2 s

To Find

Force applied.

Assumption

Let a be the acceleration.

Answer and explanation

By definition of acceleration,

$a = \frac{v - u}{t}$

Thus

$a = \frac{0 - 8}{2} = - 4$

So acceleration is -4 m/s^2

We know that

Force = Mass × Acceleration

i.e.,

F = ma

So

F = 2(-4) = -8 N

Here negative sign indicates that force is applied in opposite direction

So simply force applied was 8 N

Both way it's correct.

.............................................................................................

Answer 2

Given:-

• Mass of body (m) = 2kg

• Initial velocity (u) = 8m/s

• Final velocity (v) = 0m/s

• Time taken (t) = 2 second

To Find:-

• Force applied (F)

Solution:-

Firstly we calculate the acceleration .So,

By using 1st equation of motion

⟹ v =u +at

Put the value which is given above

⟹ 0 = 8 + a×2

⟹ -8 = a×2

⟹ a = -8/2

⟹ a = -4m/s²

here, negative sign show retardation

∴ The acceleration of body is 4m/s²

Now, Calculate the Force applied on it

⟹ Force = Mass × Acceleration

Put the value which is given above

⟹ F = 2×4

⟹ F = 8N

∴ The force applied on the body is 8 Newton.

Hence Option (a) is the correct answer.

Additional Information!!

✧ The product of mass and acceleration is called force.

✧ SI unit of Force is Newton (N).

✧ The rate of change of velocity at per unit time is called acceleration .

✧ SI unit of acceleration is m/s²

✧ It is vector Quantity ( both magnitude and direction)