Help maths questions

Hi I'm struggling with this questions. any help appreciated.
At time t seconds its distance s metres from a fixed point is given by:
s = t^3 - 12t^2 + 45t + 10
1) find velocity in terms of t
2) find acceleration in terms of t
3) find two values of t which is stationary.
4)Find value of t when acceleration is zero.

Reply 1

nuodai

Well

v=\dot s

and

a= \dot v = \ddot s

, so for (1) and (2) it's just a case of differentiating. For (3) the question doesn't make much sense -- find the values of t for which what is stationary? Take the 'what' here and differentiate it to find the corresponding t-values. For (4) you need to solve the equation

a(t)=0

for t.

Reply 2

immense010

I take it that this refers to some body, whose distance at time t is given by said formula, and that q3 refers to the 2 values of t for which said body is stationary. In that case, same as nuodai pointed out for q4, just solve v(t)=0 for t. As the function v(t) is quadratic, you'll get 2 sollutions.