Answer:
[tex]v = 5.72\ m/s[/tex]
Explanation:
given,
initial speed of the motorist = 20 m/s
distance of the traffic light = 200 m
time of which red light stays = 15 s
time taken to step on brake = 1 s
distance travel in this time
d = s x t
d = 20 x 1 = 20 m
time taken to reach the red light after reaction time= 15 -1 = 14 s
distance to travel in 14 s = 200 -20 = 180 m
to calculate the speed of the motorist when it reaches the red light.
using equation of motion
[tex]s = u t + \dfrac{1}{2}at^2[/tex]
[tex]180 =20\times 14 + \dfrac{1}{2}\times a\times 14^2[/tex]
[tex] 98 a = -100[/tex]
[tex]a = -1.02\ m/s^2[/tex]
using equation of motion to calculate the velocity
[tex]v^2 = u^2 + 2 a s[/tex]
[tex]v^2 = 20^2 - 2\times 1.02\times 180[/tex]
[tex]v = 5.72\ m/s[/tex]
Speed of motorist when it reaches red light is equal to 5.72 m/s.
