Can a particle moving with instantaneous speed 3.00 m/s on a path with radius of

Question

Can a particle moving with instantaneous speed 3.00 m/s on a path with radius of curvature 2.00 m have an acceleration of magnitude 6.00 m/s2? (b) Can it have an acceleration of magnitude 4.00 m/s2? In each case, if the answer is yes, explain how it can happen; if the answer is no, explain why not. Can a particle moving with instantaneous speed 3.00 m/s on a path with radius of curvature 2.00 m have an acceleration of magnitude 6.00 m/s2? (b) Can it have an acceleration of magnitude 4.00 m/s2? In each case, if the answer is yes, explain how it can happen; if the answer is no, explain why not.

Explanation / Answer

For the particle to make a circular turn , centripetal acceleration is required (Ac)

Ac = v^2/r

Given, v = 3 m/s , r = 2 m

So , Ac = (3)^2/2 = 4.5 m/s^2

Since the particle stays in the circular motion , tangential acceleration is also there for the particle along with centripetal acceleration

So , the magnitude of acceleration( | A | ) should be greater than the centripetal acceleration ( Ac)

| A | should be greater than 4.5 m/s^2

So the particle can have an acceleration of magnitude of

6 m/s^2 since it is greater than (Ac) = 4.5m/s^2

the particle can not have an acceleration of magnitude of

4 m/s^2 since it is less than (Ac) = 4.5m/s^2

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