Question

Problem 4. A motorcycle is moving with a velocity of 90 km/h and it takes 5 second to stop
after the brakes are applied. Calculate the force exerted by the brakes on the motorcycle if its mass
alongwith the rider is 200 kg.​

Answer 1

Answer:

• The Force (F) Exerted by the brakes is - 1000 N.

Given:

1. Initial velocity (u) = 90 Km/h
2. Final velocity (v) = 0 Km/h = 0 m/s
3. time Period (t) = 5 Sec.
4. Given Mass (M) = 200 Kg

Explanation:

$\rule{300}{1.5}$

Before solving we need to convert the units into S.I Units.

Initial velocity = ? m/s

We Know,

⇒ 1 Km/h = 5 / 18 m/s

⇒ 90 Km/h = 90 × 5 / 18

⇒ 90 Km/h = 5 × 5

⇒ 90 Km/h = 25

⇒ u = 25 m/s

$\rule{300}{1.5}$

$\rule{300}{1.5}$

From the acceleration formula,

⇒ a = ( v - u ) / t

Where,

• a Denotes Acceleration.
• v Denotes Final velocity.
• u Denotes Initial velocity.
• t Denotes Time taken.

Now,

⇒ a = ( v - u ) / t

Substituting the values,

⇒ a = ( 0 - 25 ) / 5

⇒ a = - 25 / 5

⇒ a = - 5

⇒ a = - 5 m/s²

∴ We got the acceleration.

$\rule{300}{1.5}$

$\rule{300}{1.5}$

From, Newton's Second law of motion.

⇒ F = M a

Where,

• F Denotes Force.
• M Denotes Mass.
• a Denotes Acceleration.

Now,

⇒ F = M a

Substituting the values,

⇒ F = 200 Kg × - 5 m/s²

⇒ F = 200 × - 5

⇒ F = - 1000

⇒ F = - 1000 N.

∴ The Force (F) Exerted by the brakes is - 1000 N.

Note:

• The Force & Acceleration is negative as the brakes opposes the motion of the motor cycle.

$\rule{300}{1.5}$

Answer 2

$\huge\underline\mathtt\red{Answer:-}$

The Force (F) Exerted by the brakes is - 1000 N.