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

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

The speed of the truck is

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

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

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

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

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

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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

Step by step solution

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

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

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