Question

A motorcycle is moving at velocity of 108 km per hour and takes 4second to stop when breaks are applied. Calculate the force exerted by the brakes if the mass is 1000 kg.


pls answer​

Answer 1

Answer:

Given :-

• A motorcycle is moving at velocity of 108 km/h and takes 4 seconds to stop when brakes are applied.
• The mass is 1000 kg.

To Find :-

• What is the force exerted by the brakes.

Formula Used :-

$\clubsuit$ First Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{v =\: u + at}}}$

where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = Time Taken

$\clubsuit$ Force Formula :

$\mapsto \sf\boxed{\bold{\pink{F =\: ma}}}$

where,

• F = Force
• m = Mass
• a = Acceleration

Solution :-

First, we have to convert the initial velocity km/h into m/s :

$\implies \sf Initial\: Velocity =\: 108\: km/h$

$\implies \sf Initial\: Velocity =\: 108 \times \dfrac{5}{18}\: m/s\: \: \bigg\lgroup \sf\bold{\pink{1\: km/h =\: \dfrac{5}{18}\: m/s}}\bigg\rgroup$

$\implies \sf Initial\: Velocity =\: \dfrac{540}{18}\: m/s$

$\implies \sf\bold{\purple{Initial\: Velocity =\: 30\: m/s}}$

Now, we have to find the acceleration :

Given :

• Initial Velocity (u) = 30 m/s
• Final Velocity (v) = 0 m/s
• Time Taken (t) = 4 seconds

According to the question by using the formula we get,

$\implies \sf 0 =\: 30 + a(4)$

$\implies \sf 0 =\: 30 + 4a$

$\implies \sf 0 - 30 =\: 4a$

$\implies \sf - 30 =\: 4a$

$\implies \sf \dfrac{- 30}{4} =\: a$

$\implies \sf - 7.5 =\: a$

$\implies \sf\bold{\green{a =\: - 7.5\: m/s^2}}$

Now, we have to find the force exerted by the brakes :

Given :

• Mass (m) = 1000 kg
• Acceleration (a) = - 7.5 m/s²

According to the question by using the formula we get,

$\longrightarrow \sf F =\: (1000)(- 7.5)$

$\longrightarrow \sf F =\: 1000 \times (- 7.5)$

$\longrightarrow \sf\bold{\red{F =\: - 7500\: N}}$

Here, the negetive sign represents that the force is in opposite direction.

${\small{\bold{\underline{\therefore\: The\: force\: exerted\: by\: the\: brakes\: is\: 7500\: N\: .}}}}$