To find the acceleration of the motorcycle, we can use the following equation:
v² = u² + 2as
where: v = final velocity (0 m/s, since the motorcycle comes to rest) u = initial velocity (72 km/h) a = acceleration (to be determined) s = distance covered (10 meters)
First, we need to convert the initial velocity from km/h to m/s:
u = 72 km/h * (1,000 m/1 km) * (1 h/3,600 s) u ≈ 20 m/s
Now, we can rearrange the equation to solve for acceleration (a):
0 = (20 m/s)² + 2a * 10 m
Simplifying:
0 = 400 m²/s² + 20a m
Rearranging the equation to solve for acceleration:
20a m = -400 m²/s²
a = (-400 m²/s²) / 20 m
a = -20 m/s²
Therefore, the acceleration of the motorcycle when the brakes are applied is approximately -20 m/s². The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, representing deceleration or slowing down.