If I'm asked to find the average velocity in the first 2 seconds am I require to calculate the velcolity value for t=0 too?

Question

s =2t^3-4t^2+2t-1

 

Determine the average velocity in the first 2 seconds of motion.

Answer 1

An   s vs t   curve gives us velocity curve.  To find the velocity under a finite time interval, we find the area under the curve for that interval.

 

Find the definite integral from t=0 and t=2.

 

²∫₀  (2t³ - 4t² + 2t - 1) dt

 

V(t) = ∫(2t³ - 4t² + 2t - 1) dt

 

 

Evaluate         V(2) - V(0)

 

 

Of course,  the derivative of s at t=0 is the velocity at t=0