Starting from rest, a ball of mass 5 kg experiences a constant force of 40 N for 12 s. What is the final kinetic energy (in J) of the ball after 12 s?
To find the final kinetic energy of the ball after 12 seconds, we can use the equation:
Kinetic energy = 1/2 * mass * velocity^2
To find the velocity, we can use Newton's second law of motion:
Force = mass * acceleration
Rearranging the equation gives us:
Acceleration = Force / mass
Given that the mass of the ball is 5 kg and the force is 40 N, we can calculate the acceleration:
Acceleration = 40 N / 5 kg = 8 m/s^2
Now, we can use the kinematic equation:
v = u + a * t
where:
- v is the final velocity
- u is the initial velocity (which is 0 m/s, as the ball starts from rest)
- a is the acceleration
- t is the time duration (12 s in this case)
Using the values given, we can calculate the final velocity:
v = 0 m/s + (8 m/s^2) * 12 s
v = 0 m/s + 96 m/s
v = 96 m/s
Finally, we can substitute the final velocity (96 m/s) and the mass (5 kg) into the kinetic energy equation:
Kinetic energy = 1/2 * mass * velocity^2
Kinetic energy = 1/2 * 5 kg * (96 m/s)^2
Kinetic energy = 1/2 * 5 kg * 9216 m^2/s^2
Kinetic energy = 23040 J
Therefore, the final kinetic energy of the ball after 12 seconds is 23040 Joules.