I need homework help!! please!!?

Question

Hey i got this problem in my BC calc class and i am really stuck!
i don't know if i should use the quotient rule? product rule? chain rule? or if there's even a rule!!
ans i don't know how to do it!!
Here is the problem...
A position function is given by
s=-3t^2+2t+1
where t is in seconds and s is in meters
1- find the position at t=0.57s
2- find the average velocity over the interval [0.57 , 2.5]
3-find the velocity at t=0.57
i really really really need help! please help me! and please explain it to me i really want to learn it!
and if its possible please indicate the steps :)
Thanks in advance!!
 

Answer 1

Given s = -3t^2+2t+1

1) position at t = 0.57s

s = -3(0.57)^2+2(0.57)+1

s = -3(0.3249)+1.14+1

s = -0.9747+2.14

s = 1.1653

 Recall that first derivative of positon is velocity.

s = -3t^2+2t+1

ds/dt  = -6t+2

3) velocity at t = 0.57

= -6(0.57)+2

= -1.42

2) average velocity overthe nterval [0.57,2.5]

 velocity at t = 0.57is 5.42.

velocity at t = 2.5

= -6(2.5)+2

= -13

average velocity = (-13+1.42)/(2.5-0.57)

= -11.58/1.93

= -6