A student builds an experiment model rocket with a variable thrust engine. The test flight last for 5 seconds and the rocket's altitude (in meters) is given as s(t)=1/3(t)^(3)-2t^(2)+3t+2
a) Find the velocity and acceleration of the rocket at t=4
b)When is the particle at rest?
c)When is the acceleration 0?
d)Find the altitude and the velocity at the time(s) when the acceleration is 0
e)Find the total distance traveled in the first 5 seconds

Question

A student builds an experiment model rocket with a variable thrust engine. The test flight last for 5 seconds and the rocket's altitude (in meters) is given as s(t)=1/3(t)^(3)-2t^(2)+3t+2
a) Find the velocity and acceleration of the rocket at t=4
b)When is the particle at rest?
c)When is the acceleration 0?
d)Find the altitude and the velocity at the time(s) when the acceleration is 0
e)Find the total distance traveled in the first 5 seconds

anonymous · Answer

velocity is the derivative
acceleration is the second derivative

anonymous · Answer

b)When is the particle at rest?
set the derivative equal to zero and solve

anonymous · Answer

I just want to make sure I did it right, for a I got 3m/s and 4m/s^2 but I'm not sure if it's correct

anonymous · Answer

i don't know 
the derivative is 
$$v(t)=t^2-4t+3$$ and 
$$a(t)=2t-4$$

anonymous · Answer

is $v(4)=3$?

anonymous · Answer

yup that's what I got and I got a(4)=4

anonymous · Answer

I think I got a and b but how about c?

anonymous · Answer

Solve for 0=2t-4

Get t=2

anonymous · Answer

ok thank you :) I'm kind of confused on d. How do you set it up?

anonymous · Answer

Well the original formula is the position aka altitude. So plug t=2 into that.

The first derivative is the velocity so plug t=2 into that. 

That should be what you are looking for

anonymous · Answer

ok I got it thank you :)