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

Answer:

the answer is 0.84375 mm

Step-by-step explanation:

Answer 2

ANSWER

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,

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

$s (0.75) = 0.84375$