You are attending the Summer Olympics and have been taking data of the position as a function of time of Olympic High Divers. You have determined the following position function:
You know \(g\text{,}\) the mass of the diver \(m\text{,}\) the time constant \(T\text{,}\) and the initial velocity of the diver \(\vec{v}_o = -v_o\hat{y}\text{.}\) Your goal is to determine the drag force as a function of time.
A*R*C*S7.4.2.The Sprinter.
An sprinter can be modeled as having a velocity in the \(x\)-direction of \(v_x = c\left(1 - e^{-t/b}\right)\text{.}\) What is the magnitude of the sprinter’s maximum acceleration?
Figure7.4.1.An example of using the A*R*C*S steps.
A*R*C*S7.4.3.The Rolling Cylinder.
A large cylinder rolls along flat, level ground. Because of substantial air resistance and varying amounts of friction, its speed decreases in a complicated way. Its speed as a function of time is \(v = at^2 + bt + c\text{,}\) where \(a = -2.00 \mathrm{~m/s^3}\text{,}\)\(b = -2.00 \mathrm{~m/s^2}\text{,}\) and \(c =12.0 \mathrm{~m/s}\text{.}\) How far does the cylinder move from \(t = 0 \mathrm{~s}\) until it comes to rest?
ReferencesReferences
[1]
“The Sprinter” adapted from Knight’s Physics for Scientists and Engineers.
