Question

Indefinite Integrals: To what constant deceleration would a car moving along a straight road be subjected if the car were brought to rest from a speed of 81 ft/sec in 10 sec? What would the stopping distance be?

Answer 1

A constant deceleration tells you that the velocity is linear, and so the deceleration will be equivalent to the average rate of change of the velocity:
\[a=\frac{0-81}{10-0}\]
that is, the ratio of the change in velocity to the change in time.

The second question asks what distance is covered, which would be given by
\[\int_0^{10}v(t)~dt\]
You're not explicitly given the velocity function, but you can easily find it, knowing that it's a line between the points \((0,81)\) and \((10,0)\).