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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

01

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

vc=95kmh=95kmh脳1000m1km脳1h3600s=26.39ms

The speed of the truck is

vt=75kmh=75kmh脳1000m1km脳1h3600s=20.83ms

The car is 210 m behind the truck.

Assumption.

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

02

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 dc=鈥�vc鈥�t, and the distance traveled by the truck in time t is dt=鈥�vt鈥�t.

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

vct=vtt+210mvc-vtt=210m26.39ms-20.83mst=210mt=37.77s

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

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