Question

4. A driver of a car A travelling at a uniform speed of
54 km/h for 10 s applies the brakes and decelerates
uniformly. The car stops in 5 s. Driver of car B
going at 36 km/h for 10 s applies the brakes slowly
and stops after 10 seconds. Plot the speed-time
graph of both cars and find out which of the two
cars travelled farther after the brakes were
applied ?
​

Answer 1

Given :-

For driver A :

Uniform speed of the driver = 54 km/h

Time in which the car is in 54 km/h = 10 s

Time taken for the car to come in rest when the brakes were applied = 5 s

For driver B :

Speed of the car = 36 km/h

Time in which the car is in 36 km/h = 10 s

To Find :-

Find out which of the two cars travelled farther after the brakes were applied.

Solution :-

We know that,

• b = Base
• h = Height
• s = Distance

For car A,

Distance = 1/2 × Base × Height

Given that,

Height (h) = 5 m

Base (b) = 15 m/s

Substituting their values,

⇒ s = 1/2 × 15 × 5

⇒ s = 75/2

⇒ s = 37.5

For car B,

Distance = 1/2 × Base × Height

Given that,

Height (h) = 10 m

Base (b) = 10 m/s

Substituting their values,

⇒ s = 1/2 × 10 × 10

⇒ s = 100/2

⇒ s = 50 m

Therefore,

50 > 37.5

Car B > Car A

Therefore, car B travelled further after the brakes were applied.