A strategy you will use to solve a variety of physics problems can be thought of as a sequence of steps called Chop-Multiply-Add. You can see these steps outlined in the video above for one example. Below is another example: if you know an object’s acceleration as a function of time and you want to find the change in velocity between some initial and final time.
Chop: You can start by chopping up a time interval into small pieces. Each piece of time is represented by the expression \(dt\text{,}\) where the \(d\) indicates that the actual amount of time is infinitesimally small.
Multiply: You want to know about velocity, but you know about acceleration. Although you want \(\Delta \vec{v}\text{,}\) the change in velocity over a whole time interval, you can start by trying to find an infinitesimal change in velocity \(d\vec{v}\text{.}\) By rewriting the definition of instantaneous acceleration as \(d \vec{v} = \vec{a}(t) dt\text{,}\) you can see that a way to get \(d\vec{v}\) is to multiply\(\vec{a}(t)\) and \(dt\text{.}\)
Add: Last, once you have the infinitesimal \(d\vec{v}\text{,}\) you need to add together every \(d\vec{v}\) over the full times of interest, which can be done with an integral:
Super Mario (mass \(M\)) is initially located at position xi running to the right with constant speed \(v_i\text{.}\) At \(t = 0\text{,}\) Mario finds a Super Star that results in the following force acting on him:
First find a symbolic expression for Mario’s velocity as a function of time. Then use your expression to find when Mario’s velocity is equal to \(v_i\text{.}\) Last of all, find Mario’s position.
