Question

A car moving at constant speed in a straight line with the engine providing a driving force equal to the resistive force F.

When the engine is switched off, the car is brought to rest in a distance of 100 m by the resistive force.

It may be assumed that F is constant during the deceleration.

The process is then repeated for the same car with the same initial speed but with a constant resistive force of 0.800 F.

How far will the car travel while decelerating?

A. 120 m
B. 125 m
C. 156 m
D. 250 m

Answer 1

125 b

simultaneous kinematic equations two variables are F and stopping distance

Answer 2

Answer:

Option (b)

Explanation:

Let the initial speed of the car is u and the final speed is zero. Let mass of the car is m.

Case I

Acceleartion of the car, a = - F/m

Use III equation of motion,

$v^{2} = u^{2} + 2 a s$

$0^{2} = u^{2} - 2 \frac{F}{m} \times 100$

$u^{2} = \frac{200 F}{m}$     ...... (1)

Case II

Acceleration of the car, a = - 0.8 F/m

Use III equation of motion,

$v^{2} = u^{2} + 2 a s$

$0^{2} = u^{2} - 2 \frac{0.8F}{m} \times s$

$0^{2} = u^{2} - 2 \frac{0.8F}{m} \times s$

$u^{2} = \frac{1.6F}{m} \times s$      ..... (2)

Dividing equation (2) by equation (1), we get

s = 125 m