Question

A speed skater is sliding across the ice at a speed of 19 m/s when she encounters a rough patch of ice that is 2.0 m wide. As she coasts out of the rough patch, she is moving with a speed of 18 m/s. Assuming her deceleration to be constant, roughly what is the magnitude of that deceleration?

Answer 1

Answer:

$-9.25 m/s^2$

Explanation:

The motion of the skater is a uniformly accelerated motion, so we can find the deceleration by using the following suvat equation:

$v^2-u^2=2as$

where

v is the final velocity

u is the initial velocity

a is the acceleration

s is the displacement

In this problem, we have:

u = 19 m/s is the initial velocity of the skater

v = 18 m/s is the final velocity of the skater

s = 2.0 m is the displacement

Solving for a, we can find the acceleration:

$a=\frac{v^2-u^2}{2s}=\frac{18^2-19^2}{2(2.0)}=-9.25 m/s^2$

And the negative sign tells us that the acceleration is in the opposite direction to the motion (so, it is a deceleration)