Crall and Whipple attached a fan to a cart placed on a level track and then released the cart. They made a position-versus-time graph (see figure below) and fit a curve to these data such that
x = 0.036 m + (0.0080 m/s)t + (0.10 m/s2)t2.
(a) Find the velocity as a function of time. (Use the following as necessary: t. Do not enter units in your answer.)
v = dx/dt = 0.0080 + 0.20t
To find the velocity as a function of time, you can calculate the derivative of the position equation with respect to time. In this case, the position equation is:
x = 0.036 m + (0.0080 m/s)t + (0.10 m/s^2)t^2.
Taking the derivative, you can find the velocity equation:
v = d(x)/dt.
Differentiating each term separately, you get:
v = 0 + 0.0080 m/s + 2(0.10 m/s^2)t.
Simplifying, the velocity equation as a function of time is:
v = 0.0080 m/s + 0.20 m/s^2 t.
Therefore, the velocity equation is v = 0.0080 + 0.20t.