Question

A motorcyclist completed half of the circle with speed 10 ms–1, next quarter with speed 60 ms–1 and the final quarter with 30 ms–1. What is the average speed of the motorcycle?

Answer 1

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Answer 2

Answer:

The average speed of the motorcycle is 20 ms⁻¹.

Explanation:

Given:

Let the total distance of the journey to be 3x and let the t₁, t₂ and t₃ be the time intervals in the first half, first quater and second quater respectively.

• For the first half, speed is given as 10 ms⁻¹.

        ∴  $Time= \frac{Distance }{Time} = \frac{x}{10}=t_{1}$

• For the first quater, speed is given as 60 ms⁻¹.

       ∴  $Time= \frac{Distance }{Time} = \frac{x}{60}=t_{2}$

• For the second quater, speed is given as 30 ms⁻¹.

       ∴  $Time= \frac{Distance }{Time} = \frac{x}{30}=t_{3}$

Now,

$Average speed = \frac{Total distance}{Total time}$

$Average speed = \frac{3x}{t_{1}+t_{2}+t_{3} }$

$Average speed = \frac{3x}{\frac{x}{10}+\frac{x}{60}+\frac{x}{30} }$

$Average speed = \frac{3x}{\frac{9x}{60} }$

$Average speed = \frac{3x}{9x }$ × $60$

$Average speed = \frac{60}{3}$

$Average speed = 20 ms^{-1}$

Therefore, the average speed of the motorcycle is 20 ms⁻¹.

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