Question

A figure skater skates across a rink of length 50 m in 12.1 seconds. a. What is the average speed of the skater? (2 points) b. It takes the figure skater 2 seconds to increase her speed from 4 m/s to 5.3 m/s. What is the acceleration of the skater? (2 points) c. The skater is moving at a speed of 13 m/s when she starts to brake. She comes to a stop after traveling a distance of 8 m. What was her acceleration? (2 points)

Answer 1

(a) The skater covers a distance of S=50 m in a time of t=12.1 s, so its average speed is the ratio between the distance covered and the time taken:

`v= (S)/(t)= (50 m)/(12.1 s)=4.13 m/s`

(b) The initial speed of the skater is

`v_i = 4 m/s`
while the final speed is

`v_f = 5.3 m/s`
and the time taken to accelerate to this velocity is t=2 s, so the acceleration of the skater is given by

`a= (v_f - v_i)/(t)= (5.3 m/s-4.0 m/s)/(2.0 s)=0.65 m/s^2`

(c) The initial speed of the skater is

`v_i = 13.0 m/s`
while the final speed is

`v_f=0`
since she comes to a stop. The distance covered is S=8 m, so we can use the following relationship to find the acceleration of the skater:

`2aS=v_f^2 -v_i^2`
from which we find

`a= (-v_i^2)/(2S)= (-(13.0m/s)^2)/(2 \cdot 8.0 m)=-10.6 m/s^2`
where the negative sign means it is a deceleration.