Question

An object is traveling around a circle with a radius of 20 meters. If in 10 seconds a central angle of 1/5 radian is swept out, what is the linear speed of the object?

Answer 1

The linear speed is 0.4 m/s

Explanation:

Given,

The radius of the circle = 20 meters,

The central angle made by the object that travelling around the circle =
`(1)/(5)` radian,

So, the distance covered by the object = The radius of the circle × Central angle made by the object ( in radians )

`=20* (1)/(5)`

`=4\text{ meters}`

Now, the time taken by the object in travelling = 10 seconds,

`\text{Speed}=\frac{\text{Distance}}{\text{Time}}`

Hence, the linear speed of the object =
`(4)/(10)`

= 0.4 m/s

Answer 2

The linear speed of the object is the ratio between the measure of the arc it had traveled and the time. For the length of the arc,
2π x (20 m) x (0.2 rad/ 2π rad) = 4 meters
Divide this by the time, 10 s. Thus, the linear speed is equal to 0.4 m/s.