Question

a motorcar is moving with a velocity of 108 km/h and it takes 4s to stop after applied the brakes on the motorcar if it's mass along with the passengers is 1000 kg.​

Answer 1

Correct Question:

A motorcar is moving with a velocity of 108 km/h and it takes 4 s to stop after the brakes are applied. Calculate the force exerted by the brakes on the motorcar if its mass along with the passengers is 1000 kg.

Step-by-step explanation:

Given :-

• Mass of the motor car along with passengers (m)= 1000 kg
• Initial velocity (u) = 108 km/h
• Time taken (t) = 4 s

To find :-

• The force exerted by the brakes on the motor car.

Solution :-

Since the car stops, the final velocity (v) will be 0 m/s.

• Initial velocity (u) = 108 km/h.

Converting initial velocity into m/s.

We know that, $\sf{1\:km/h=\dfrac{5}{18}\:m/s}$.

Then initial velocity,

= [108 × 5/18 ] m/s

= 30 m/s

Now find the force exerted by the brakes.

★ Formula used :

${\boxed{\sf{F=\dfrac{m(v-u)}{t}}}}$

• [put values]

$: \implies \sf \: F= \dfrac{1000(0 - 30)}{ 4} \\ \\ : \implies \sf \: F \: = \dfrac{ - 30000}{4} \\ \\ : \implies \sf \: F \: = - 7500$

• The force exerted by the brakes on the motor car = -7500 N.

The negative sign of force(F) means that the force was applied in opposite direction of motion.

__________________

Answer 2

Answer:

$\tt {\pink{We \: have}}\begin{cases} \sf{\green{Initial \: Velocity \: (u) =108 \: km/hr}}\\ \sf{\blue{Time \: taken \: (t) =4 \: seconds}}\\ \sf{\orange{Mass \: along \: with \: the \: passengers=1000 \: kg}}\\ \sf{\red{Force= \: ?}}\end{cases}$

$\qquad \tiny \dag \: \underline{ \tt Changing \: Initial \: Velocity \: km/hr \: into \: m/s \: we \: get :}$

$\dashrightarrow\:\:\sf Initial \: Velocity = 108 \times \dfrac{5}{18}$

$\dashrightarrow\:\: \sf Initial \: Velocity = 30 \: m/s$

$\qquad\tiny\dag \: \tt \underline{Now, we \: will \: find \: force \: exerted \: by \: the \: brakes \: on \: motor car : }$

$:\implies\sf Force = Mass \times \Bigg\lgroup\dfrac{Initial \: Velocity - Final \: Velocity}{Time} \Bigg \rgroup$

$:\implies\sf Force = 1000 \times \dfrac{0 - 30}{4}$

$:\implies\sf Force = 1000 \times \dfrac{- 30}{4}$

$:\implies\sf Force = \dfrac{ - 30000}{4}$

$:\implies \underline{ \boxed{\sf Force = - 7500 \: \:Newtons }}$

$\therefore\underline{\textsf{The force exerted by the brakes on the motorcar is \textbf{ -7500 Newtons}}}.$