The Problem:
A long-jumper takes a run of 30 metres to accelerate to a speed of 10 m/s from a standing start. Find the time he takes to reach this speed, and hence calculate his acceleration. Illustrate his run-up with a velocity-time graph.
Douglas Quadling Mechanics 1
Exercise 1B Q4
Step 1: Find the time taken to reach 10 m/s
We are given:
- Initial velocity, u = 0 m/s (standing start),
- Final velocity, v = 10 m/s,
- Distance covered, s = 30 m.
We use the kinematic equation:
v² = u² + 2as
Substitute the known values:
10² = 0² + 2a(30)
100 = 60a
a = 100 / 60 = 1.67 m/s²
Now, use the equation v = u + at to find the time t:
t = (v – u) / a = (10 – 0) / 1.67 = 6 seconds
Step 2: Calculate acceleration
From the above calculation, the acceleration is:
a = 1.67 m/s²
Final Answers:
- Time taken to reach 10 m/s: t = 6 seconds,
- Acceleration: a = 1.67 m/s².
