Question

A car moving along a straight highway with speed of 126 km h-1 is brought to a stop within a distance of 200 m. What is the retardation of the car (assumed uniform), and how long does it take for the car to stop?

Answer 1

Given :-

A car moving along a straight highway with speed of 126 km h-1.

It is brought to a stop within a distance of 200 m.

To Find :-

The retardation of the car.

Time required for the car to stop.

Solution :-

We know that,

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

Let's consider,

The initial velocity of the car = u

Final velocity of the car = v

Using 3rd equation of motion,

$\underline{\boxed{\sf v^2-u^2=2as}}$

Given that,

u = 126 km/h = 35 m/s

Substituting their values,

a = (v² - u²)/2s

= (0 - 35²)/2 × 200

= –1225/400

= –3.06 m/s²

Using the formula,

$\underline{\boxed{\sf Time=\dfrac{(Final \ velocity-Initial \ velocity)}{Acceleration} }}$

Given that,

Distance covered by the car before coming to rest = 200 m

Initial velocity = 0

Substituting their values,

0 = 35 – 3.06 × t

= 35/3.06

= 11.43 sec

Therefore, is takes 11.43 sec for the car to stop.