Question

A car moving with a speed of 108 km/h come to rest after for 4 second on applying brakes .if the mass of the car in including the passenger is 1000 kg what will be the force applied when brakes applied

Answer 1

Given :

• Initial velocity (u) = 108 km/h
• Final velocity (v) = 0 m/s
• Time (t) = 4 seconds
• Mass of the car (m) = 1000 kg

To find :

• Force applied

According to the question,

Note : We have to change 108 km/h into m/s. So, it will be 30 m/s.

By using Newton's first equation of motion we will find acceleration then by using F = ma we will find force,

⇒ v = u + at

Where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

⇒ Substituting the values,

⇒ 0 = 30 + a × 4

⇒ 0 - 30 = 4a

⇒ - 30 = 4a

⇒ - 30 ÷ 4 = a

⇒ - 7.5 = a

So,the acceleration ia - 7.5 m/s². Negative signs means retardation.

Now,

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

⇒ Force = Mass × Acceleration

Or,

⇒ F = ma

⇒ Substituting the values,

⇒ F = 1000 × (-7.5)

⇒ F = - 7500 N

So,the force applied is - 7500 Newtons.

Note :- The negative signs shows that this force is acting on opposite direction.

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Answer 2

Given -

• Initial velocity (u) = 108 km/h
• Final velocity (v) = 0 m/s
• Time = 4s
• Mass of the car including the mass of passengers = 1000 kg

To find -

• Force applied when brakes are applied.

Solution -

• Firstly, convert the Initial velocity from km/h to m/s

As we know,

↬ 1 h = (60 × 60)s

↬ 1 km = 1000 m

• Divide by 3600s and multiply by 1000.

$\sf{\dfrac {108 \times 1000}{60 \times 60}}$

= 30 m/s

• Initial velocity = 30 m/s

• Find acceleration first to find the force applies when brakes are applied.

• v = u + at

Substitute the given values -

↬ v = u + at

↬ 0 = 30 + a × 4

↬ -30 = a × 4

↬ $\sf{\dfrac{-30}{4}}$ = a

↬ - 7.5 = a

Acceleration = 7.5 m/$\sf{s^2}$

• Retardation = 7.5 $\sf{m/s^2}$

• F = ma

where,

F = force

m = mass

a = acceleration

Substitute the given values.

↬ F = 1000 × (-7.5)

↬ F = - 7500 N

• Force applied = - 7500 N

• Answer = - 7500 N