Question

a circular cycle track has a circumference of 314 m with AB as the diameter . a cyclist travel from A to B along the circular path with a constant velocity of magnitude 15.7 m/s. find the time taken.​

Answer 1

Given :

• Circumference of circular track = 314m.
• Velocity of cyclist along semi-circular path = 15.7 ms¯¹.
• AB is diameter of the track.

To Find :

• Time taken by the cyclist from A to B

Formula used :

• Speed = distance /time

Solution :

★Refer to figure in the attachment.★

As we know,

$Circumference \: of \: circle = 2\pi r$

Then,

$314 = 2 \times 3.14 \times r \\ \\ \frac{314}{2 \times 3.14} = r \\ \\ 50 = r$

Now, As given the cyclist travells from A to B in a semi-circle, so the distance covered by it will be ;

→$\frac{Circumference}{2}$

→$\frac{314}{2}$

→ $517$

Hence,

$Speed = \frac{distance}{time} \\ \\ 15.7 = \frac{157}{time} \\ \\ time = \frac{157}{15.7} = 10 \: sec$

Therefore, the time taken by the cyclist travelling from A to B is 10 seconds.