Question

an automobile travelling with a speed of 60km/hr ,can brake to stop within a distance of 20 m . if the car is going twice as fast ,i.e. 120 km/hr ,the stopping distance will be ?

Answer 1

Answer on Question #44622, Physics, Mechanics | Kinematics | Dynamics

An automobile travelling with a speed of $60\mathrm{km/hr}$, can brake to stop within a distance of $20\mathrm{m}$. If the car is going twice as fast, i.e. $120\mathrm{km/hr}$, the stopping distance will be?

Solution:

Kinematics equation

$$2ad = v^2 - v_0^2$$

where $a$ is acceleration, $d$ is distance, $v_0$ is initial velocity and $v$ is final velocity.

The acceleration is the same in both cases.

Thus,

$$a = \frac{-v_0^2}{2d}$$

So,

$$\frac{v_{01}^2}{2d_1} = \frac{v_{02}^2}{2d_2}$$ $$d_2 = \left(\frac{v_{02}}{v_{01}}\right)^2 d_1 = \left(\frac{120}{60}\right)^2 20 = 4 \cdot 20 = 80\ \mathrm{m}$$

Answer: $d_2 = 80\ \mathrm{m}$

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