Question

A car traveling at 95 km/h is 210 m behind a truck traveling at 75 km/h. How long will it take for the car to reach the truck?

Short answer

The car takes 37.77 s to reach the truck.

Step-by-step solution

Step 1. Finding the car’s and truck’s velocity in the SI unit

The velocity of a body is defined as the displacement of the body in unit time. The velocity of a body is a scalar quantity and has the same unit as that of speed.

Given data.

The speed of the car is

$\begin{array}{c}{v}_{\mathrm{c}}=95\frac{\mathrm{km}}{\mathrm{h}}\\ =95\frac{\mathrm{km}}{\mathrm{h}}\times \frac{1000\mathrm{m}}{1\mathrm{km}}\times \frac{1\mathrm{h}}{3600\mathrm{s}}\\ =26.39\frac{\mathrm{m}}{\mathrm{s}}\end{array}$

The speed of the truck is

$\begin{array}{c}{v}_{\mathrm{t}}=75\frac{\mathrm{km}}{\mathrm{h}}\\ =75\frac{\mathrm{km}}{\mathrm{h}}\times \frac{1000\mathrm{m}}{1\mathrm{km}}\times \frac{1\mathrm{h}}{3600\mathrm{s}}\\ =20.83\frac{\mathrm{m}}{\mathrm{s}}\end{array}$

The car is 210 m behind the truck.

Assumption.

Assume that the car takes t time to reach the truck.

Step 2. Calculation of the time using the relation between distance, speed, and time

Then, the distance traveled by the car in time t is $d_{\mathrm{c}}= v_c t$, and the distance traveled by the truck in time t is $d_{\mathrm{t}}= v_{\mathrm{t}} t$.

Now, after t time, they are in the same position. Then,

$\begin{array}{c}{v}_{\mathrm{c}}t=v_{\mathrm{t}}t+210\mathrm{m}\\ \left(v_{\mathrm{c}}-v_{\mathrm{t}}\right)t=210\mathrm{m}\\ \left(26.39\frac{\mathrm{m}}{\mathrm{s}}-20.83\frac{\mathrm{m}}{\mathrm{s}}\right)t=210\mathrm{m}\\ t=37.77\mathrm{s}\end{array}$

Therefore, the car takes 37.77 s to reach the truck.