Physics with calculus

Question

An object moves along the y axis in feet. The position function is s(t)=t^3-6t^2+9t. find the instantaneous velocity of the object at times 2 seconds and 5 seconds. Find the times at which the object is stationary, that is fine the times when v(t)=0

Answer 1

s(t) = t³ - 6t² + 9t

 

v(t) = ds/dt = 3t² - 12t + 9

 

Evaluate v(2) and v(5) to get the instantaneous speeds at 2 and 5 seconds.

 

Set v(t) = 0 and solve the quadratic equation for t to get times when object is instantaneously at rest.  From this point on, it is an algebra problem, and you should be able to finish the solution.