Kinematics And Derivatives

Step 1: Find the velocity and acceleration.
The velocity is the first derivative of the displacement: The acceleration is the derivative of the velocity:

Step 2: Find the time when acceleration is 14 .
Set the acceleration equal to 14 and solve for :

Step 3: Find the velocity and displacement at .
Substitute into the velocity equation: Substitute into the displacement equation:

Final Answer: At , the velocity is and the displacement is .