f(t)=-4.9t^2+25t+3 meters
what is the average velocity during the first two seconds?
find the instantaneous velocity at t=2
average velociy = (f(2) - f(0))/2
for instant.
take derivative, sub in t = 2
To find the average velocity during the first two seconds, we need to find the displacement of the object during that time interval and divide it by the duration.
The displacement is given by the equation f(t) = -4.9t^2 + 25t + 3. We need to find the displacement between t = 0 and t = 2.
Substituting t = 2 into the equation, we get:
f(2) = -4.9(2)^2 + 25(2) + 3
= -4.9(4) + 50 + 3
= -19.6 + 50 + 3
= 33.4
So, the displacement during the first two seconds is 33.4 meters.
The duration is 2 seconds.
Average velocity = displacement / duration
= 33.4 meters / 2 seconds
= 16.7 meters/second
Therefore, the average velocity during the first two seconds is 16.7 meters/second.
To find the instantaneous velocity at t = 2, we can take the derivative of the position function f(t) with respect to t and evaluate it at t = 2.
The derivative of f(t) = -4.9t^2 + 25t + 3 is:
f'(t) = -9.8t + 25
Substituting t = 2 into the derivative, we get:
f'(2) = -9.8(2) + 25
= -19.6 + 25
= 5.4
Therefore, the instantaneous velocity at t = 2 is 5.4 meters/second.