Question

A runner runs around a track consisting of two parallel lines 96 m long connected at th
he completes one lap in 100 seconds. What is her average velocity?
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Answer 1

$\huge{\underline{\underline{\boxed{\sf{\purple{Answer ࿐}}}}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

• ❝ $\small{\underline{\underline{\boxed{\sf{\green{5 m/s }}}}}}$ ❞

Step-by-step explanation:

• First task is to find the total length of the track.We know it's made out of 2 straight lines of 96 m long ... and 2 semicircles with a radius of 49 m.

• Since we have TWO semicircles, we can say we have one circle... so we can calculate its circumference:

$\small \underline {\sf{C \ = \ 2 \ x \ π \ x \ r \ = \ 2 \ x \ 3.14 \ x \ 49 = 307.72 m }}$

• This is for the both semicircles at the ends.

• Now, let's add the two 96 m long straight lines to get the full length of the track:

$\small \underline {\sf{ T = 307.72 + 96 + 96 = 499.72 m}}$

• Now that we have the total length of the track, we can easily calculate her average speed.

• She does one lap in 100 seconds, so her average speed/velocity is:

$\small \underline \orange {\sf{ S = 499.72 m / 100 s = 4.9972 m/s }}$$\small \underline \orange {\sf{or \ 5 m/s \ if \ we \ round \ up \ a \ bit }}$

Answer 2

Answer:

5 m/s.‍♂️

Explanation:

Average velocity is displacement divided by time interval of the displacement.

To find the displacement, we need to find the length of the track.

The track consists of two parallel lines and two semicircles.

The length of each parallel line is 96 m.

The circumference of a circle is 2πr, where r is the radius.

So, the circumference of a semicircle is πr.

The radius of each semicircle is 49 m.

So, the length of each semicircle is π * 49 m.

Using pi = 22/7, we get:

The length of each semicircle = (22/7) * 49 m

= 154 m

Therefore, the length of the track = 2 * (96 + 154) m

= 500 m

The displacement is equal to the length of the track because the competitor finishes a complete round.

So, Δx = 500 m

The time interval for this displacement is given as 100 seconds.

So, Δt = 100 s

Using the formula for average velocity:

vˉ = Δx / Δt

= 500 / 100

= 5 m/s

Therefore, the magnitude of its average velocity is 5 m/s.‍♂️