Question

A particle travels along the curve from A to B in 5 s. It takes 8 s for it to go from B to C and then 10 s to go from C to A. Determine its average speed when it goes around the closed path.

Answer 1

Answer:

5.1 m/s

Explanation:

The figure is missing: find it in attachment.

In order to find the average speed, we have to calculate the length of the total path, and divide it by the total time elapsed.

The curve from A to B is a quarter of a circle with a radius of r = 20 m, so its length is:

$AB=\frac{\pi r}{2}=\frac{\pi (20)}{2}=31.4 m$

The path BC is the hypothenuse of a right triangle with sides equal to 20 m and 30 m, so its length is

$BC=\sqrt{30^2+20^2}=36 m$

Finally, the length of the path AC is the sum of the side of 30 m and the radius of the curve, so

$AC=30 + 20 = 50 m$

So the total distance covered is

$d=AB+BC+AC=31.4+36+50=117.4 m$

The total time elapsed is

$t=5 s + 8 s + 10 s =23 s$

So, the average speed is

$v=\frac{d}{t}=\frac{117.4}{23}=5.1 m/s$