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.
The first equation of motion is given as:
v = u + at …….(i)
where,
v is the final speed of the body,
u is the initial speed of the body,
a is the acceleration of the body.
t is the time taken by the body.
Given,
Mass of the three-wheeler, M = 400 kg
Mass of the driver, m = 65 kg
Initial speed of the three-wheeler, u = 36 km/h
Final speed of the three-wheeler, v = 0 km/h
Time taken by the vehicle to completely stop, t = 4 sec
Total mass of the system= M + m= 400+65 = 465 kg
From equation (i), 
⇒ 
Here, the negative sign indicates that the body is retarding and the velocity of the system is decreasing with the time.
From Newton’s second law of motion, the magnitude of the force is given as,
F= (M + m)× a
= 465 kg × (-2.5 m/s2) = -1162.5 N
The negative sign indicates that the force is acting in the opposite direction of the motion of the three-wheeler.
The average retarding force on the vehicle is 1162.5 N