The equation of motion of a particle is s = t^3 - 3t, where is in meters and is in seconds.

Question

Find the acceleration when the velocity is 0.

 

I know the function for acceleration is 6t so I thought the answer must be 0. However, the back of the book says the answer is 6. Is that an error?

Answer 1

To find the acceleration when the velocity = 0, you need to know when (at what time) that occurs. Since v = ds/dt, we have

 

v = 3t² - 3

v(t₀) = 0 = 3t₀² - 3

 

Call this value t₀ = 1. Then go back to the expression for acceleration and plug it in:

 

a = d²s/dt² = 6t

a(t₀) = 6(1) = 6.

Answer 2

The velocity is 3t^2-3, so you have to set this function equal to zero and solve for t. 

 

After that, you plug the t value to 6t