The Problem:
A marathon competitor running at 5 m/s puts on a sprint when she is 100 metres from the finish, and covers this distance in 16 seconds. Assuming that her acceleration is constant, use the equation s= = (u+v)t to find how fast she is running as she crosses the finishing line.
Douglas Quadling Mechanics 1
Exercise 1B Q
A marathon competitor running at 5 m/s puts on a sprint when she is 100 metres from the finish and covers this distance in 16 seconds. Assuming that her acceleration is constant, use the equation s = (u + v)t / 2 to find how fast she is running as she crosses the finishing line.
Solution:
Step 1: Rearrange the Equation
The equation of motion is:
s = (u + v) t / 2
Rearrange to solve for v:
v = (2s / t) - u
Step 2: Substitute the Known Values
Given:
- Distance (s) = 100 m
- Initial speed (u) = 5 m/s
- Time (t) = 16 s
Substitute into the equation:
v = (2 * 100) / 16 - 5
Simplify:
v = 200 / 16 - 5
v = 12.5 - 5
v = 7.5 m/s
Final Answer: The competitor is running at 7.5 m/s as she crosses the finishing line.
