Plane Curvilinear Motion: n-t Coordinates - Example Problem 3.3-7
A motorcycle travels in a circular path having a radius of 200 ft at a speed of 45 mph. For a short distance from s = 0, the motorcycle increases its speed, from its initial 45 mph, by dv/dt = 0.5s ft/s2, where s is in feet. Determine its speed and the magnitude of its acceleration when it has moved to s = 30 feet.
Given:
- ρ = 200 ft
- v = 45 mph = 66 ft/s
- dv/dt = 0.5s ft/s2
- so = 0
- sf = 30 ft
Find:
- vf
- af
Video solution:
The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.
Interactive solution:
Curved path motion is usually analyzed using either the n-t or r-θ coordinate systems. When analyzing a problem, using either of these coordinate systems, it is very important to assign each know quantity to the correct variable. In the n-t system it is crucial to differentiate between a and dv/dt. dv/dt is equal to the tangential component of a.
Knowing the tangential acceleration (i.e. dv/dt), what equation should we use to determine the speed of the motorcycle?