A skateboarder, starting from rest, rolls down a 14.0-m ramp. When she arrives at the bottom of the ramp her speed is 8.00 m/s.
(a) Determine the magnitude of her acceleration, assumed to be constant.
To determine the magnitude of the skateboarder's acceleration, we can use the equation of motion that relates acceleration, initial velocity, final velocity, and displacement:
v^2 = u^2 + 2as
Where:
v = final velocity (8.00 m/s)
u = initial velocity (0 m/s, as she starts from rest)
a = acceleration (what we want to find)
s = displacement (14.0 m)
Rearranging the equation to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Plugging in the given values:
a = (8.00^2 - 0^2) / (2 * 14.0)
Simplifying,
a = (64 - 0) / 28.0
a = 64 / 28.0
a ≈ 2.286 m/s^2
Hence, the magnitude of the skateboarder's acceleration is approximately 2.286 m/s^2.