A car stopped at a red light starts moving when the light turns green and accelerates at the rate of 2.7 m/s2 for 15 seconds. The driver continues at this speed for two minutes, until he sees the next traffic signal turning red 191 m away. He reacts after 2 seconds and slams on his brakes. a. What is the car’s acceleration if he stops just as he reaches the light? b. What is the total distance covered by the car?
Answers
Answer:
see the attachment and answer
Given: acceleration = 2.7ms⁻²
time = 15 second
time for which velocity remains constant = 2 minute
distance covered when stopped = 191 m
To find: (a) acceleration of the car if he stops just as he reaches the light
(b) total distance covered by a car.
Solution:
Final velocity of the car after he sees the green light is given by (v-u) = at
initial velocity is zero, therefore, (v - 0) = 2.7×15
Final velocity = 40.5 ms⁻¹
Distance covered will be given by v² - u² = 2aS
(40.5)² - 0 = 2×2.7×S
S = 303.75m
Now, the car travels at the constant velocity for about 2 minutes ( 120 seconds), so the distance covered in this time = vt
= 40.5 × 120 = 4860 m.
(a) When he sees the light, the car stops, so the acceleration will be zero.
(b) Distance covered by the car will be = 303.75 + 4860 + 191 m
= 5354.75 m