Question

he driver of a car travelling at 72 kmph observes the light 300 m ahead of him turning red. The traffic light is timed to remain red for 20 s before it turns green. If the motorist wishes to passes the light without stopping to wait for it to turn green, determine:

(i) the required uniform acceleration of the car;
(ii) the speed with which the motorist crosses the traffic light.

Answer 1

so using formula s = ut + 1/2 at² 
where s = displacement = 300 m
t = time = 20 s
a = acceleration= a (let)
u = initial velocity= 75 km/h
so 
300 = 75 × 20 + 1/2 ×a × 400
solving for a so a = 0.75 m/s² 
so the required uniform acceleration of the car is 0.75 m/s² 
using formula v² = u² + 2as
where 
a = acceleration= 0.75 m/s²
u = initial velocity= 75 km/h
s = displacement = 300 m
so v² = 75² +2 × 0.75 × 300
solving for v = 77.94 m/s
so the speed with which the motorist crosses the traffic light is v = 77.94 m/s

Answer 2

The above answer is incorrect.

First, the initial speed is not 75 km/h but 72 km/h.

Secondly, we calculate in meters per second and not kilometers per hour, so u = 72 / 3.6 = 20.

Hence, the first equation:

300 = 20 * 20 + 1/2 * a * 20^2

a = -0.5 m/s/s

the second:

v^2 = 20^2 + 2 * -0.5 * 300

v = 10 m/s or 36 km/h