Particle Velocity and Acceleration Equations for Position Function s(t)

[1irishman]

Homework Statement

When will the velocity be zero?
t is in minutes
s is in metres

Homework Equations

s = 4t^3 - 8t^2 + t - 50

The Attempt at a Solution

I came up with the velocity equation by taking the derivative of function s.
I came up with the acceleration equation by taking the derivative of the velocity function. I don't know how to figure out(solve) when the velocity of the particle will be zero? Help please?
The velocity at t minutes is given by:
v(t) = 12t^2 - 16t + 1
Acceleration is given by:
a(t) = 24t - 16

 

[Doc Al]

The velocity at t minutes is given by:
v(t) = 12t^2 - 16t + 1

Looks good. So plug in the value for v and solve the equation for t.

 

[1irishman]

can i use quadratic formula, like this?

t = -b + - sqrt b^2 - 4ac/2a

where a = 12, b = -16, and c = 1 ?

 

[thepatient]

Exactly, that will give you the times at which v(t) = 0

 

[Doc Al]

can i use quadratic formula, like this?

t = -b + - sqrt b^2 - 4ac/2a

where a = 12, b = -16, and c = 1 ?

Yes!

 

[1irishman]

My answer came to be:

t = 16 + - sqrt208/24

but the answer in the back of book is 4 + - sqrt13/6

I am not sure how they got that?

 

[Ecthelion]

Try simplifying your square root expression more that you already have, and you'll find you have the same answer.

 

[1irishman]

oh yes thank you i see 16*13 = 208