The vertical position of an object is modeled by the function h(t)=-16t^2 +5t+7, where h is measured in feet and t is measured in seconds. Find the object's initial velocity (that is, the velocity at t=0).
Is it 5 feet per second?
yes
v(t) = h ' (t) = -16t + 5
so
v(0) = -16(0) + 5 = 5
To find the object's initial velocity, we need to determine the derivative of the position function with respect to time, h'(t).
Given the position function h(t) = -16t^2 + 5t + 7, we can differentiate it to find h'(t):
h'(t) = -32t + 5
Now, to find the initial velocity, we substitute t = 0 into the expression for h'(t):
h'(0) = -32(0) + 5
= 0 + 5
= 5
Therefore, the object's initial velocity is 5 ft/s.
To find the object's initial velocity, we need to determine the value of h'(0), where h'(t) represents the derivative of the function h(t) with respect to time.
To find the derivative of h(t), we can differentiate each term of the function separately. The derivative of -16t^2 is -32t, the derivative of 5t is 5, and the derivative of 7 (a constant) is 0. Therefore, the derivative of h(t) is h'(t) = -32t + 5.
Now, to find h'(0), we substitute t = 0 into the equation: h'(0) = -32(0) + 5 = 5.
Thus, the object's initial velocity is 5 feet per second.