Question

The position of a particle moving along a coordinate line is given by s = 2t³ - 3t² + 4t, with s in meters and t in seconds. Find the particle's velocity and acceleration at t = 2 sec.

Answer 1

Differentiate the position function to find the velocity and acceleration functions, then substitute t = 2 sec to find the values at that time.

Step-by-step explanation:

To find the particle's velocity and acceleration at t = 2 sec, we need to differentiate the position function with respect to time. The velocity function is the derivative of the position function, and the acceleration function is the derivative of the velocity function.

So, differentiate s = 2t³ - 3t² + 4t to find the velocity function. Then differentiate the velocity function to find the acceleration function.

Once we have the velocity and acceleration functions, we can substitute t = 2 sec to find the velocity and acceleration at that time.