Answer:
a) v = t² -18 t + 64, a = 2 t - 18, b) a = -18 m / s², c) a = -2 m / s²
Explanation:
In this exercise they tell us the function of position with respect to time
s = ⅓ t³ - 8 t² + 64 t + 3
a) find the velocity and acceleration.
For this we use the definition of velocity and acceleration
v = ds / dt
a = dv / dt
we make the derivatives
v = t² -18 t + 64
a = 2 t - 18
b) for this part we substitute t = 1
a = 2 1 -18
a = -18 m / s²
c) let's find the time for which v = 0
0 = t² - 18 t + 64
this expression is a binomial or perfect
(x + a) ² = x² + 2 a x + a²
in this case
x = t
a = 8
(t-8) ² = t² - 16 t + 64
therefore the velocity is zero for when t = 8 s
the acceleration at this point is
a = 2 8 - 18
a = -2 m / s²
