Physics help?

Question

x(t)=(3.0t^2 -2.0t+3.0)m
from this info how do I find the average speed between t=2 and t=3 and the instantaneous time at t=2.
please give me the step by step process.

Thanks in advance.

Answer 1

Find x(t) at t=2 and t=3. Divide their difference (distance) by the time (1 second) and that's the 'average' speed.
Vavg = (x(2) - x(3))/(1 sec.)

To get velocity, take the derivative of x(t) with respect to t to get
x'(t) = 6t - 2 and then plug in t=2 to get x'(2) = 10 m/s

Doug