Question

A cyclist completes half round of circular track of radius 318 m in 1.5 minute. Find its speed and velocity.

Answer 1

Answer:

Speed = 10.75 m/s

Velocity = 7.06 m/s

Explanation:

Speed is defined as the ratio of total distance traveled to Total time taken.

Velocity is defined as the ratio of total displacement to Total time taken.

Here, we are given that the cyclist has traveled half round of circular track.

Radius of track, r = 318 m

Time taken, t = 1.5 min = 90 sec

Please refer to attached image.

Total distance traveled here = Perimeter of Half Circle.

Distance = $\pi \times r$

$\Rightarrow \dfrac{22}{7} \times 318 = 22 \times 44 = 968\ m$

$Speed = \dfrac{Total\ Distance\ Traveled}{Time\ Taken}\\\Rightarrow Speed = \dfrac{968}{90}\\\Rightarrow Speed = 10.75\ m/s$

Total Displacement here = AB which is the diameter of circular path

So, Displacement = 2 $\times$ 318 m = 636 m

Hence,

$Velocity = \dfrac{Total\ Displacement}{Time\ Taken}\\\Rightarrow Velocity = \dfrac{636}{90}\\\Rightarrow Velocity = 7.06\ m/s$

So, answers are:

Speed = 10.75 m/s

Velocity = 7.06 m/s