Question

A car travelling at 60 km/h overtakes another car travelling at 42 km/h . assuming each car to be 5 .0 m long. Find the time taken during the overtake.

Answer 1

A car travelling at $60~\mathrm{km/h}$ overtakes another car travelling at $42~\mathrm{km/h}$. Assuming each car to be $5.0~\mathrm{m}$ long. Find the time taken during the overtake.

Relative velocity of cars equals:

$$v_{12} = v_1 - v_2 - \text{because one overtakes another}$$

where $v_1, v_2$ - velocities of first and second cars.

Their total length equals:

$$L = 2l,$$

where $l$ - length of one car (their lengths equal)

Therefore, time taken during the overtake equals:

$$t = \frac{L}{v_{12}} = \frac{2l}{v_1 - v_2} = \frac{10~\mathrm{m}}{(60 - 42)^{\frac{\mathrm{km}}{\mathrm{h}}}} = \frac{10~\mathrm{m}}{5^{\frac{\mathrm{m}}{2}}} = 2~\mathrm{s}$$

Answer: $t = 2$ seconds