ANSWER
0.84375 mm
EXPLANATION
The velocity function is given by:
[tex]v = 6t - 6 {t}^{2} [/tex]
To find the displacement function, we integrate:
[tex]s = \int \: 6t - 6 {t}^{2}d t[/tex]
[tex]s (t) = 3 {t}^{2} - 2 {t}^{3} + c[/tex]
The initial displacement is zero.
This implies that,
[tex]3 {(0)}^{2} - 2 {(0)}^{3} + c = 0[/tex]
[tex]c = 0[/tex]
This gives us,
[tex]s (t) = 3 {t}^{2} - 2 {t}^{3} [/tex]
After t=0.75s,
[tex]s (0.75) = 3 {(0.75)}^{2} - 2 {(0.75)}^{3} + c[/tex]
[tex]s (0.75) = 0.84375[/tex]
