A skater increases her speed uniformly from 2.0 meters per second to 7.0 meters per second over a distance of 12 meters. What is the magnitude of her acceleration?A 1.9 m/s2B 2.2 m/s2C 2.4 m/s2D 3.8 m/s2
Question
A skater increases her speed uniformly from 2.0 meters per second to 7.0 meters per second over a distance of 12 meters. What is the magnitude of her acceleration?A 1.9 m/s2B 2.2 m/s2C 2.4 m/s2D 3.8 m/s2
Solution
To solve this problem, we can use the equation of motion that relates final speed, initial speed, acceleration, and distance. The equation is:
v^2 = u^2 + 2as
where: v = final speed u = initial speed a = acceleration s = distance
We can rearrange the equation to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = ((7.0 m/s)^2 - (2.0 m/s)^2) / (2 * 12 m) a = (49 m^2/s^2 - 4 m^2/s^2) / 24 m a = 45 m^2/s^2 / 24 m a = 1.875 m/s^2
So, the closest answer is A, 1.9 m/s^2.
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