Question

A girl jogs around a horizontal circle with a constant speed. She travels one fourth of a revolution, a distance of 25 m along the circumference of the circle, in 5.0 s. The magnitude of her acceleration is

Answer 1

Answer:

The centripetal acceleration of the girl is 2.468 m/s²

Explanation:

Given;

number of turns, = ¹/₄ Revolution

distance traveled by the girl, d = 25 m

time of motion, t = 5.0 s

The linear speed of the of the girl is calculated as;

$v = \omega \ r\\\\v =(\frac{1}{4}rev \times \frac{2\pi \ rad}{1 \ rev} \times \frac{1}{5 \ s} ) (25 \ m)\\\\v = (0.3142 \ \frac{rad}{s} )(25 \ m)\\\\v = 7.855 \ m/s$

The centripetal acceleration of the girl is calculated as;

$a_c = \frac{v^2}{r} \\\\a_c = \frac{(7.855)^2}{25} \\\\a_c = 2.468 \ m/s^2$

Therefore, the centripetal acceleration of the girl is 2.468 m/s²