CB.Calc.CHA-4.C: Determine values for positions and rates of change using definite integrals in problems involving rectilinear motion.

Determine values for positions and rates of change using definite integrals in problems involving rectilinear motion.

Example Problems

As a particle moves along the number line, its acceleration is

a(t) = 6t - 12

.
If

v(1) = 4

and

s(1) = 10

, what is the position function

s(t)

?

A particle with velocity

v(t) = \sin(t)

, where

t

is time in seconds, moves in a straight line.
How far does the particle move from

t = 0

to

t = \frac{\pi}{2}

seconds?

A particle with velocity

v(t) = \sin(2t)

, where

t

is time in seconds, moves in a straight line.
How far does the particle move from

t = 0

to

t = \frac{\pi}{2}

seconds?

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