A motorcycle and a car start from rest from the same place at the same time and travel in the same direction.
The motorcycle accelerates at 1.0 m/s^2 up to a speed of 36 km/h and the car at 0.5 m/s^2 up to a speed of 54 km/h .The time at which the car would overtake
the motorcycle is
Answers
Answer:
car will overtake bike after 35 sec
Explanation:
The distance from starting point, where bike reaches it final speed 10 m/s is given by
v2 = 2×a×S ; hence S = v2/(2a) = 100/2 = 50 m
Time t1 for the bike to reach final velocity = v/a = 10/1 = 10 s.
The distance from starting point, where car reaches it final speed 15m/s is given by
v2 = 2×a×S ; hence S = v2/(2a) = 225/(2×0.5) = 225 m ................................(1)
Time t2 for the car to reach final velocity = v/a = 15/0.5 = 30 s.
In this 30 s duration of car travel, distance travelled by bike = Initial 50 m in 10 s + distance travelled in 20 s with uniform speed 10 m/s
= 50 + 20×100 = 250 m ............................(2)
From (1) and (2), we know that after 30 s the distance between car and bike = 25 m.
After 30 s , both bike and car are moving with uniform speed. Car speed is 15 m/s and bike speed is 10 m/s.
hence additional time to cover this 25 m gap = 25/(15-10) = 5 s.
total time is 30+5 = 35 s.
Car will overtake bike after 35 s