Answer to Question #208351 in Physics for lindsay

Question

An object is pushed from rest across a sheet of ice, accelerating at 5.0 m/s² over a distance of 80.0 cm. The object then slides with a constant speed for 4.0 s until it reaches a rough section which causes it to stop in 2.5 s. (6 marks)

1. What is the speed of the object when it reaches the rough section?
2. At what rate does the object slow down once it reaches the rough section?
3. What total distance does the object slide throughout its entire trip?

Answer 1

1. The speed is

$$v=\sqrt{2ah}=\sqrt{2·5·0.8}=2.83\text{ m/s}^2.$$

2. The deceleration is

$$a=\frac vt=\frac{2.83}{2.5}=1.13\text{ m/s}^2.$$

3. Acceleration (0.8 m), constant motion 4 s at 2.83 m/s, i.e. 11.3 m, and deceleration 1.13 m/s² during 2.5 s:

$$D=0.8+11.3+\frac{2.83·2.5}{2}=15.6\text{ m}.$$