A truck and a car are moving with equal velocity. If equal retarding force is applied on each, then on applyin

Question

A truck and a car are moving with equal velocity. If equal retarding force is applied on each, then on applying the brakes both will stop after certain distance:

Accepted Answer

1. **Analyze using Work-Energy Theorem:** The work done by the retarding force ($F$) in stopping the vehicle over a distance ($s$) is equal to the initial kinetic energy ($K$) of the vehicle.
   $$ W = F \cdot s = K = \frac{1}{2}mv^2 $$
   [Source 144]
2. **Derive Relationship:** Rearranging for distance $s$:
   $$ s = \frac{mv^2}{2F} $$
3. **Compare Variables:**
   - Initial velocity ($v$) is the same for both.
   - Retarding force ($F$) is the same for both.
   - Therefore, the stopping distance is directly proportional to the mass: $s \propto m$.
4. **Conclusion:** Since the mass of the truck ($m_{truck}$) is greater than the mass of the car ($m_{car}$), the stopping distance for the truck will be greater ($s_{truck} > s_{car}$). Consequently, the car will cover less distance before coming to rest.

Step-by-Step Solution

Practice All PHYSICS Questions