A jogger runs at a constant speed of 17.2 m/s around a circular track of radius

Question

A jogger runs at a constant speed of 17.2 m/s around a circular track of radius 222 meters. The jogger runs counter-clockwise and starts and ends at the places depicted in the sketch and the angle x = 59.7 degrees. If the time it takes for the jogger to run from the start to the end is 3.6 seconds, what is the magnitude of the average acceleration of the jogger in m/s2? (Hint: there is only one equation for average acceleration so just find the x and y components of the initial velocity and final velocity and use those to find the average acceleration. To find the components of the final velocity vector, use geometry using the "hints" given on the sketch - at the end point, I've sketched an important right angle.)

Explanation / Answer

If we are to assume that the diagram, which you have not inserted, is: that the angle is with relative to the x axis, and the runner starts at the place where theta = 59.7 degrees, then the only acceleration possible would be centripedal acceleration - the problem did state "CONSTANT SPEED". So it has to be centripedal acceleration. So, the equation for that is - ac = vt2/r. So we know vt, we know r, so all we have to do is plug it in -

ac= vt2/ r

ac = 17.22/ 222

ac = 1.3326 m/s2

For some reason, all of your other values were not used. The only explanation for that would be that you typed the problem wrong - instead of "runs at a constant speed", I think it said "runs at a initial velocity". Hope this helped.

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