Question:medium

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

Updated On: Jan 21, 2026
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Solution and Explanation

Given:

Initial speed of the car,
u = 126 km h−1 = 35 m s−1

Final speed of the car,
v = 0 (car comes to rest)

Distance covered before stopping,
s = 200 m

Motion is with uniform retardation.

Step 1: Calculate the retardation

Using the equation of motion:

v2 = u2 + 2as

Substitute the given values:

0 = (35)2 + 2a(200)

0 = 1225 + 400a

a = −1225 / 400

a = −3.06 m s−2

(The negative sign indicates retardation.)

Step 2: Calculate the time taken to stop

Using the equation:

v = u + at

0 = 35 − 3.06t

t = 35 / 3.06

t ≈ 11.4 s

Final Answer:

Retardation of the car = 3.06 m s−2
Time taken by the car to stop = 11.4 s

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