Question

If a runner runs a race on a circular track that has a radius of 30 m and they complete the race in 125 seconds, but they end the race at the same spot they started, what would be the difference between the runner's SPEED and VELOCITY?

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Answer 1

1.51 m/s

Step-by-step explanation:

Given

Radius of the track r = 30 m

Time taken t = 125 s

Solution

A) Speed

Speed = Distance / time

Since distance is the total length of the path, the circumference of the circle is the distance travelled

`S = 2\pi r/t\\\\S = 2 * 3.14 * 30/125\\\\S = 1.51 m/s`

B) Velocity

Velocity = Displacement / time

Displacement is the shortest distance between the starting and end point. Since the starting and end points are the same. The shortest distance between them will be zero.

Since the displacement is zero the velocity is also zero.

V = 0/125 = 0 m/s

C) Difference between speed and velocity

S - V = 1.51 - 0

S - V = 1.51 m/s

Answer 2

To answer this question you must know that speed is only one magnitude, but velocity is a magnitude with an associated direction, that is, it is a vector.

For a circular movement like the one shown in the problem the velocity is defined as:

`V = wr[-sin(\theta) x + cos (\theta)y]`

Where:

w = angular velocity

r = radius of the circumference

`\theta` = angle of the object with respect to the origin

Speed is defined as:

`v = |V|\\\\v = wr`.

In this problem we know that:

r = 30 m

`w = (1\ turn)/(125)\ s^(-1)\\\\w = (2\pi)/(125)\ s^(-1)\\\\w = 0.0503\ s^(-1)`

So:

v = | V | = wr

v = (0.0503)(30)

v = 1.5079 m/s speed of the runner

On the other hand:

`V = 1.5079 [-sin(\theta)x + cos(\theta)y]\ m/s` velocity of the runner