Question

Calc Help

Answer 1

The position function of a particle in rectilinear motion is given by s(t) = t3 – 12t2 + 45t + 4 for t ≥ 0.Find the position and acceleration of the particle at the instant the when the particle reverses direction. Include units in your answer.

Answer 2

Your question asks "Find the position and acceleration of the particle at the instant the when the particle reverses direction. "


When the particle reverses direction, we know the velocity equals zero.

Answer 3

Do you know how to get from the position equation to the velocity equation?

Answer 4

take the derivative?

Answer 5

correct. Take the derivative of the position equation and you''ll get the velocity equation.

Answer 6

3t^2-24t+45

Answer 7

But we want to know what t is when the V(t)=0

Answer 8

so set the derivative = 0

Answer 9

I got t=3 and t=5

Answer 10

We know that the position
\(s(t) = t^3 – 12t^2 + 45t + 4 \)
and we also know that \( s′(t) = v(t) \)
So, \(s′(t) = v(t) =3t^2-24t+45\)

Answer 11

What does t=3 and t=5 represent?

Answer 12

when the velocity is 0

Answer 13

t=3 and t=5 is the seconds when the velocity is zero

Answer 14

Now