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 -1 and the car at 0.5 m s -2 up to a speed of 54 km h -1 .The time at which the car would overtake the motorcycle is
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When car overtakes motorcycle, both have travelled the same distance in the same time. Let the total distance raveled be S and the total time taken to overtake be t. For motor cycle :
Maximum speed attained 
Since its acceleration 
the time 
taken by it to attain the maximum speed is given by
( 
)
The distance covered by motorcycle in attaining the maximum speed is
The time during which the motorcycle moves with maximum speed is (t-10)s.
The distance covered by the motorcycle during this time is
Total distance travelled by motorcycle in time t is
= (10t - 50)m …… (i)
For car
Maximum speed attained 
Since its accelerations 
The times taken by it to attain the maximum speed is given by
( 
)
Or 
The distance covered by the car in attaining the maximum speed is
The time during which the car moves with maximum speed is (t -30)s.
The distance covered by the car during this time is
Total distance travelled by car in time t is
= (15t - 225)m …… (ii)
From equations (i) and (ii), we get
10t – 50 = 15t – 225 or 5t = 175 or t = 35s
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