To find the acceleration of the motorcycle, we can use the following kinematic equation:
v^2 = u^2 + 2as
Where: v = final velocity (0 m/s since the motorcycle comes to rest) u = initial velocity (72 km/h * r) a = acceleration s = distance covered (10 meters)
First, let's convert the initial velocity from km/h to m/s: 72 km/h * r = 72 * r * (1000 m/3600 s) = 20 * r m/s
Now, we can plug the values into the equation and solve for acceleration:
0 = (20 * r)^2 + 2 * a * 10
Simplifying: 0 = 400 * r^2 + 20 * a
Rearranging the equation: 20 * a = -400 * r^2
Finally, we can solve for acceleration: a = (-400 * r^2) / 20 = -20 * r^2
Therefore, the acceleration of the motorcycle is -20 * r^2 (in m/s²).