Question

An object moves along the x axis according to the equation x = 3.00t^2 - 2.00t + 3.00 where x is in meters and t is in seconds.

Determine the average speed between t = 2.00 s and t = 3.00s

Answer 1

x = 3 t² - 2 t + 3

When t=2 sec, x = 3 (4) - 2 (2) + 3
= 12 - 4 + 3 = 11 meters .

When t=3 sec, x = 3 (9) - 2 (3) + 3
= 27 - 6 + 3 = 24 meters .

Distance = (end position) - (start position) = (24m - 11m) = 13 meters

Time = (end time) - (start time) = (3s - 2s) = 1 second

Speed = (distance) / (time) = 13 meters / 1 sec = 13 meters/second

Answer 2

We are given the equation:

x = 3 t² - 2 t + 3
We use that equation to calculate for the distance traveled.

At t=2 sec, x = 3 (4) - 2 (2) + 3
x =11 meters

At t=3 sec, x = 3 (9) - 2 (3) + 3
x = 24 meters

Velocity = (24 meters - 11 meters) / (3 s - 2 s ) = 13 m/s