The driver of a car travelling at a speed of 20 m/s, wishes to overtake a truck that is moving with a constant speed of 20 m s –1 in the same lane. The car’s maximum acceleration is 0.5 m s –2 . Initially the vehicles are separated by 40 m, and the car returns back into its lane after it is 40 m ahead of the truck. The car is 3 m long and the truck 17m long.
(i) Find the minimum time required for the car to pass the truck and return back to its lane?
Text Solution
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(i) Displacement of car relative to truck
x r = 40 + 17 + 3 + 40
= 100 m.
Initilly
Relative initial velocity between car and truck
u r = 20 – 20 = 0
Finally
Relative acceleration between car and truck
a r = 0.5 – 0 = 0.5 m/s 2
Let required time = t .
∴ II equation of motion
x r = u r .t + 
a r .t 2
⇒ 100 = 0 + 
× 0.5 × t 2
⇒ t = 20 sec.
(ii) Distance travelled by car
x c = ut + 
at 2
= 20 × 20 + 
× 0.5 × 20 2
= 500m
(iii) Final speed of the car
= u + at
= 20 + 0.5 × 20 = 30m/s.
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