A child rides a pony on a circular track whose radius is 5.25 m. a) Find the distance traveled and the displacement after the child has gone halfway around the track. b) Does the distance traveled increase, decrease or stay the same when the child completed one circuit of the track?

a) Distance is a scalar quantity that tells you how much space a body has covered when moving. Displacement is a vector quantity that tells you how far from its initial position and object is after moving.

In this case, the child goes around the track only halfway from point 1 to point 2. We know the circunference or perimeter of a circle to be 2*PI*radius. We also know the child only when halfway, so we need to divide the perimeter by 2, thus we get distance = PI*radius

distance halfway = (PI)*(5.25) = 16.49 [m]

And now that we know the definition of displacement, we can easily see that the child went from point 1 to point 2 which is located at a distance of 1 diameter from point 1:

displacement halfway = D = 2*radius = 2(5.25) = 10.5 [m]

b)What happens to the distance when the child completes one circuit? The distance will increase beause he is now completing the circuit so he is covering more ground in his movement:

distance circuit = 2*(PI)*radius = 2(PI)(5.25) = 32.99 [m]

32.99 is more than 16.49 so we are certain that the distance increases.