Final answer:
The magnitude of the average force needed to stop a bicycle and its rider with a mass of 80 kilograms moving at 6.0 meters per second in 4.0 seconds is 120 newtons.
Step-by-step explanation:
The question asks for the magnitude of the average force required to bring a bicycle and its rider with a combined mass of 80 kilograms, moving at a speed of 6.0 meters per second, to a stop in 4.0 seconds. To find this, we use the formula for force based on Newton's second law of motion, F = ma, where F is force, m is mass, and a is acceleration.
First, we calculate the acceleration needed to stop the bicycle in the given time. Since the final velocity is 0 m/s (because the bicycle stops), we can calculate acceleration as a = (Vf - Vi) / t, where Vf is final velocity, Vi is initial velocity, and t is time. Substituting the given values:
a = (0 m/s - 6.0 m/s) / 4.0 s = -1.5 m/s². The negative sign indicates that the acceleration is in the opposite direction of the initial velocity (deceleration).
Now, applying this acceleration to the formula for force, we get: F = m * a = 80 kg * (-1.5 m/s²) = -120 N. The magnitude of this force is 120 newtons; the negative sign is omitted when considering magnitude.