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 initia…

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asked Mar 16, 2020 187k views

2 Answers

AD WAN · Answer 1 · 2020-03-22T08:49:06+0000

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