2.5 Distance, Velocity, Acceleration & Other

Distance, Velocity, Acceleration & Other

Distance, Velocity, and Acceleration

s(t) = distance at time t

v(t) = velocity at time t

a(t) = acceleration at time t

v(t) = s’(t)

a(t) = v’(t)

A.1: A delivery truck is driving along a straight road, and after t hours its distance (in miles) east of its starting point is

for 0 < t < 6. Find the velocity of the truck after 2 hours and after 5 hours. Find the acceleration of the truck after 1 hour.

A.2: A helicopter rises vertically, and after t seconds its height above the ground is

feet (0 < t < 6). Find the velocity after 2 seconds and after 5 seconds. Find the acceleration after 1 second.

More Interpretations of the Second Derivative

The second derivative has other meanings besides acceleration. In general, the second derivatives measure how the rate of change is itself changing. That is, the second derivative tells whether the rate is speeding up or slowing down.

A.3: Demographers predict that t years from now the population of a city will be:

Find P’(8) and P’’(8) and interpret these numbers.


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