Q11. A car traveling at 95 km/h is 21... [FREE SOLUTION]

Chapter 2: Q11. (page 43)

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

Expert verified

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

$\begin{matrix} v_{c} = 95 \frac{km}{h} \\ = 95 \frac{km}{h} 脳 \frac{1000 m}{1 km} 脳 \frac{1 h}{3600 s} \\ = 26.39 \frac{m}{s} \end{matrix}$

The speed of the truck is

$\begin{matrix} v_{t} = 75 \frac{km}{h} \\ = 75 \frac{km}{h} 脳 \frac{1000 m}{1 km} 脳 \frac{1 h}{3600 s} \\ = 20.83 \frac{m}{s} \end{matrix}$

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 $d_{c} = 鈥� v_{c} 鈥� t$ , and the distance traveled by the truck in time t is $d_{t} = 鈥� v_{t} 鈥� t$ .

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

$\begin{matrix} v_{c} t = v_{t} t + 210 m \\ (v_{c} - v_{t}) t = 210 m \\ (26.39 \frac{m}{s} - 20.83 \frac{m}{s}) t = 210 m \\ t = 37.77 s \end{matrix}$