A skateboard with mass M rolls down a ramp, starting from rest. It takes time T to roll a distance L along the ramp. In terms of M, T, and L, what is the skateboard’s acceleration down the ramp?
To find the skateboard's acceleration down the ramp, we can use the equation of motion:
L = (1/2) * a * T^2
Here, L is the distance traveled, a is the acceleration, and T is the time taken.
Rearranging the equation, we can solve for a:
a = (2 * L) / (T^2)
Therefore, the skateboard's acceleration down the ramp is given by:
a = (2 * L) / (T^2)
To find the skateboard's acceleration down the ramp, we can use the kinematic equation:
L = (1/2) * a * T^2
Where:
L is the distance traveled along the ramp,
a is the acceleration of the skateboard down the ramp,
and T is the time it takes to travel distance L.
To isolate the acceleration, we rearrange the equation:
2L = a * T^2
Divide both sides of the equation by T^2:
2L / T^2 = a
So, in terms of M, T, and L, the skateboard's acceleration down the ramp would be:
a = 2L / T^2
M is irrelevant
at acceleration a, v = a T
L = (1/2) a T^2
a = 2 L/T^2