A jogger

bill
12th grade
calculus student

At time t=0 a jogger is running at a velocity of 300 meters per minute. The jogger is slowing down with a negative acceleration that is directly propotional to time t. This brings the jogger to a stop in 10 minutes.

a) write an expression for the velocity of the jogger at time t.

b) what is the total distance traveled by the jogger in that 10-minute interval.

Hi Bill,

If the velocity function is v(t) and the acceleration function is a(t) then you know a couple of facts. First, since "at time t=0 a jogger is running at a velocity of 300 meters per minute" you know that

v(0) = 300 meters/min Second, since "the jogger is slowing down with a negative acceleration that is directly propotional to time t", a(t) = -kt meters/min² where k is a positive constant.

Since a'(t) = v(t), antidifferentiate a(t) to find v(t) and then use the first fact to evaluate the constant that arises in the antidifferentiation. The constant k can then be evaluated from the fact thet the jogger's velocity is reduced to zero in 10 minutes.

Cheers,
Harley Go to Math Central