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Question
The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.
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Solution
Initial speed of the three-wheeler, u = 36 km/h
= 36 × (5/18) m/s
= 10 m/s
Final speed of the three-wheeler, v = 0 m/s
Time, t = 4 s
Mass of the three-wheeler, m = 400 kg
Mass of the driver, m' = 65 kg
Total mass of the system, M = 400 + 65 = 465 kg
Using the first law of motion, the acceleration (a) of the three-wheeler can be calculated as:
v = u + at
`:. a =(v-u)/t = (0 - 10)/4 = -2.5 "m/s"^2`
The negative sign signifies that the velocity of the three-wheeler is reducing over time.
Using Newton’s second law of motion, the net force acting on the three-wheeler can be calculated as:
F = Ma
= 465 × (-2.5) = -1162.5 N = 1.2 × 103 N
The negative sign suggests that the force is applied in opposition to the direction of motion of the three-wheeler.
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