For a track and field athlete who can jump vertically, his distance above the ground is given by the formula s = 3.3t - 4.9t2. What is his initial velocity?
velocity in m/s =
My Answer
S'= 3.3-9.8t
S'(0) = 3.3
velocity in m/s = 3.3
Can you please confirm this answer
Thanks
To find the initial velocity, we need to calculate the derivative of the position equation with respect to time. The derivative represents the velocity function.
Given: s = 3.3t - 4.9t^2
To find the derivative, we differentiate each term separately. Using the power rule of differentiation, we get:
s' = (3.3)t^0 - 2(4.9)t^1
s' = 0 - 9.8t
Here, s' represents the velocity function. Now, to find the initial velocity, we substitute t = 0 into the velocity function:
v(0) = -9.8(0)
v(0) = 0
Therefore, the initial velocity is 0 m/s. This means the athlete starts from rest before jumping vertically.