A motorcycle with a mass of 350 kg is accelerated from rest to a velocity of 30 m/s by a force of 4000 N. calculate the distance over which this acceleration occurred.
To calculate the distance over which the acceleration occurred, we can use the equations of motion.
First, we need to find the acceleration of the motorcycle, using Newton's second law of motion:
Force = mass × acceleration
Rearranging the equation to solve for acceleration, we have:
acceleration = Force / mass
Plugging in the given values, we get:
acceleration = 4000 N / 350 kg
= 11.43 m/s²
Next, we can use the following equation of motion to calculate the distance:
Distance = (initial velocity² - final velocity²) / (2 × acceleration)
Given that the initial velocity is 0 m/s (since the motorcycle starts from rest), and the final velocity is 30 m/s, we can substitute these values along with the calculated acceleration:
Distance = (0 m/s)² - (30 m/s)² / (2 × 11.43 m/s²)
Simplifying further:
Distance = 0 - 900 / (22.86 m/s²)
= -900 / (22.86 m/s²)
= -39.31 m
The negative sign indicates that we have to consider the direction of the acceleration.
Therefore, the distance over which this acceleration occurred is approximately 39.31 meters in the opposite direction of the acceleration.