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.
Solution and Explanation
Initial speed of the three-wheeler, u = 36 km/h
Final speed of the three-wheeler, v = 10 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:
\(\text v\)= \(\text u+\text {at}\)
\(\therefore\) \(\text a\) = \(\frac{v-u}{t}\)= \(\frac{0-10}{4}\) = -2.5 \(m/s^2\)
The negative sign indicates that the velocity of the three-wheeler is decreasing with time.
Using Newton’s second law of motion, the net force acting on the three-wheeler can be calculated as:
\(\text F\) = \(\text {ma}\)
\(\text F\) = 465 × (–2.5) = –1162.5 N
The negative sign indicates that the force is acting against the direction of motion of the three-wheeler.
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