Question

A truck of mass 5000 kg is moving with
speed 62 km/h, the driver of the truck applied
the brake and it come to rest in 5 sec. Find
the force applied by the brake

Answer 1

Required Answer :

The force applied by the brake = - 17,000 N

Given :

• Mass of a truck = 5000 kg
• Initial velocity of the truck = 62 km/h
• Final velocity of the truck = 0 m/s [The final velocity of the truck is zero because it comes to rest.]
• Time = 5 seconds

To find :

• Force applied by the brake

Solution :

Firstly, we will convert the initial velocity of the truck from km/h into m/s. For that multiply the value by 5/18.

⇒ Initial velocity = 62 × 5/18

⇒ Initial velocity = 31 × 5/9

⇒ Initial velocity = 155/9

⇒ Initial velocity = 17.22 m/s or 155/9 m/s

Now, we will calculate the acceleration of the truck by using the first equation of motion.

First equation of motion :

• v = u + at

where,

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

we have,

• v = 0 m/s
• u = 155/9 m/s
• t = 5 seconds

Substituting the given values :

⇒ 0 = 155/9 + a × 5

⇒ 0 = + 5a

⇒ - 155/9 = 5a

⇒ - 155/9 × 1/5 = a

⇒ - 31/9 = a

⇒ - 3.4 = a

Acceleration of the truck = - 3.4 m/s²

Now, we will calculate the force applied by the brakes :

⇒ Force = ma

where,

• m = mass
• a = acceleration

Substituting the given values :

⇒ Force = 5000 × (-3.4)

⇒ Force = - 17,000

Therefore, the force applied by the brake = - 17,000 N