Vehicle Braking Distance Calculation: Physics Example

Question:

A driver applies brakes on seeing a traffic signal 400 m ahead. At the time of applying the brakes the vehicle was moving with a speed of 15 ms^-1 and retarding with 0.3 ms^-2 .What is the distance of the vehicle after one minute from the traffic signal?

Solution- Braking distance

Time taken for the vehicle to come to stop

Applying the first equation of motion

$${v=u+at}$$

$${0=15+(-0.3)t}$$

$${15=0.3t}$$

$${t=\frac{15}{0.3}}$$

$${t=\frac{150}{3}}$$

$${t=50 \ sec}$$

Distance travelled during this time

Applying the second equation of motion

$${s=ut+\frac{1}{2}at^2}$$

$${s=(15)(50)+\frac{1}{2}(-0.3)(50^2)}$$

$${s=750-375=375 \ m}$$

Distance remaining to the signal

$${400-375 =25 \ m}$$

Key result:

The distance of the vehicle from the traffic signal after 1 minute is 25 m.