Cheryl is riding on the edge of a merry-go-round, 2m from the center, which is rotating with an increasing angular speed. cheryl’s tangential acceleration is 3.0m/s2. at the instant that cheryl’s linear speed is 4.0m/s, what is cheryl’s total acceleration?

In circular motion we know that there is two type of acceleration that Cheryl experience

1. Tangential acceleration

2. Centripetal acceleration

here given that

for centripetal acceleration we know that

now we know that both centripetal acceleration and tangential acceleration is perpendicular to each other

so total acceleration is vector sum of both and given as

so total acceleration is 8.54 m/s^2

explanation:

newton's third law, for every action there is an equal and opposite reaction.

true tan speed = ang vel x radius