Question

During each cycle, the velocity (v in mm/s) of a piston is v=6t-6t^2, where t is the time in seconds. Find the displacement "s" of the piston after .75 s if the initial displacement is zero.

Answer 1

the answer is 0.84375 mm

Explanation:

Answer 2

0.84375 mm

EXPLANATION

The velocity function is given by:

`v = 6t - 6 {t}^(2)`

To find the displacement function, we integrate:

`s = \int \: 6t - 6 {t}^(2)d t`

`s (t) = 3 {t}^(2) - 2 {t}^(3) + c`

The initial displacement is zero.

This implies that,

`3 {(0)}^(2) - 2 {(0)}^(3) + c = 0`

`c = 0`

This gives us,

`s (t) = 3 {t}^(2) - 2 {t}^(3)`

After t=0.75s,

`s (0.75) = 3 {(0.75)}^(2) - 2 {(0.75)}^(3) + c`

`s (0.75) = 0.84375`