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Question
An automobile engine propels a 1000 kg car (A) along a levelled road at a speed of 36 km h–1. Find the power if the opposing frictional force is 100 N. Now, suppose after travelling a distance of 200 m, this car collides with another stationary car (B) of the same mass and comes to rest. Let its engine also stop at the same time. Now the car (B) starts moving on the same level road without getting its engine started. Find the speed of the car (B) just after the collision.
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Solution
Here, mass of the car A, mA = 1000 kg
Initial speed of the car A, uA = 36 km h_1
= `36 xx 5/18`
= 10m s−1
Opposing frictional force, F = 100 N
∴ Power of the engine of car A
= F µA = (100 N) × (10 m s−1) = 1000 W
When car A collides with car B of mass 1000 kg,
Final speed of car A, vA = 0
Initial speed of car B, uB = 0
Applying conservation of momentum, P, = P,
mAvA + mBuB = mAvA + mBvB
1000 × 10 + 1000 x 0 = 1000 × o + 1000 × vB
∴ vB = 10m s−1
So, the speed of the car B just after the collision is 10m s−1
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