Question:

The driver of a three-wheeler moving with a speed of 36 Kmh^-1 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:

Average retarding force calculation:

Initial velocity: Conversion from Kmh^-1 to ms^-1

$${36 \ \frac{Km}{h}=36 (\frac{5}{18}) \ \frac {m}{s}}$$

$${Initial \ velocity = 10 \ \frac{m}{s}}$$

To find the acceleration:

$${Acceleration \ a =\frac{v-u}{t}}$$

Initial velocity u=10 ms^-1

Final velocity v= 0

Time taken (t) = 4.0 s

$${Acceleration=\frac{0-10}{4}}$$

$${a=-2.5 \ \frac{m}{s^2}}$$

Negative sign indicates the acceleration is in the direction opposite to that of motion (Retardation/deceleration).

Total mass of the vehicle and driver:

$${400+65 =465}$$

To find the retarding force:

$${F=ma}$$

$${F= (465)(-2.5)}$$

$${F=-1162.5 N}$$

Conclusion

The average retarding force on the vehicle is -1162.5 N

Concept of retarding force:

Retarding force is a force that acts in the direction opposite to the motion of an object, causing it to slow down.Retarding force reduces the kinetic energy of an object.Retarding force is helpful in understanding and analysing the motion of objects.Common examples are friction,air resistance and viscous drag.

Retarding forces are critical in designing the braking system for vehicles,slowing down skydivers for safe landing and in sports it is helpful in designing sports equipments.