Question

Two cars of unequal masses use similar tires. If they are moving at the same initial speed, the minimum stopping distance is:

• A. Is smaller for the heavier car
• B. Is smaller for the lighter car
• C. Is same for both cars
• D. Depends on the value of the car

Answer 1

The correct option is C Is same for both cars

Minimum distance covered upon application of brakes will not depend upon the mass of the vehicle.

As in the question it is mentioned that both the tyres are of same material, it will provide the same

amount of frictional force. And we know Frictional force $F=\mu mg$

where $\mu$=coefficient of friction, m= mass of the object and g=acceleration due to gravity.

Frictional Force $f_1=\mu m_{1}g$ and

retardation force $F_{R1}=\frac{\mu m_{1}g}{m_1}$ =$\mu g$-------(1)

Frictional force$f_2=\mu m_{2}g$ and

retardation force$F_{R2}=\frac{\mu m_{2}g}{m_2}$=$\mu g$------(2)

From 1 and 2 we can say that the amount of retardation force applied on the vehicle is same.

Now from equation of motion we get

$v^2=u^2+2as$-----------(A)

$u_1=u_2$ (given)

$v_1=v_2$ as both the vehicle stops

Hence its acceleration will also be same

Now in equation A three physical quantities are same viz. initial and final velocity and acceleration.

Thus we can conclude that both the car will cover the same distance to stop