An object moves to the right according to the equation
x = 4t2 + 3t + 16
where x is in meters and t is in seconds. Determine the object's average velocity between time t = 0 and time t = 4 seconds.
To determine the object's average velocity between time t = 0 and time t = 4 seconds, we need to find the displacement of the object during that time interval. The displacement is the change in position of the object: x(final) - x(initial).
Let's calculate the object's position at t = 0 seconds:
x(0) = 4(0)^2 + 3(0) + 16 = 16
Now, let's calculate the object's position at t = 4 seconds:
x(4) = 4(4)^2 + 3(4) + 16 = 112 + 12 + 16 = 140
Now that we have the initial position (x(initial) = 16) and the final position (x(final) = 140), we can calculate the displacement:
Displacement = x(final) - x(initial) = 140 - 16 = 124
The object's average velocity is then the displacement divided by the time interval:
Average velocity = Displacement / Time interval
Time interval = t(final) - t(initial) = 4 - 0 = 4 seconds
Average velocity = 124 / 4 = 31 meters/second
Therefore, the object's average velocity between t = 0 and t = 4 seconds is 31 meters/second.