The Problem:
A cyclist comes to the top of a hill 165 metres long travelling at 5 m s, and free-wheels down it with an acceleration of 0.8 ms 2. Write expressions for his speed and the distance he has travelled after seconds. Hence find how long he takes to reach the bottom of the hill, and how fast he is then travelling.
Douglas Quadling Mechanics1 Exercise1C Q
A boy kicks a football up a slope with a speed of 6 m/s. The ball decelerates at 0.3 m/s². How far up the slope does it roll?
Solution:
- Initial speed (u) = 6 m/s
- Deceleration (a) = -0.3 m/s² (negative because it’s slowing down)
- Final speed (v) = 0 m/s (the ball stops at the highest point)
Using the equation of motion:
v² = u² + 2as
Rearranged to solve for distance (s):
s = (v² - u²) / (2a)
Plugging in the values:
s = (0 - 36) / (2 * -0.3)
s = -36 / -0.6
s = 60 meters
Answer: The football rolls 60 meters up the slope before coming to rest.
