Question 4

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

Given:

Initial speed, $$v_1=60\ \frac{km}{h}$$

Stopping distance, d1=20 m

New speed, $$v_2=120km/h$$

Braking distance is proportional to the square of speed:

$$d\propto v^2$$

Therefore,

$$\frac{d_2}{d_1}=\left(\frac{v_2}{v_1}\right)^2$$

Substituting the values:

$$\frac{d_2}{20}=\left(\frac{120}{60}\right)^2$$

$$\frac{d_2}{20}=2^2$$

$$\frac{d_2}{20}=4$$

$$d_2=20\times4$$

$$d_2=80m$$

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