Starting from rest, a ball of mass 3 kg experiences a constant force of 21 N for 12 s. What is the final kinetic energy (in J) of the ball after 12 s?
dcsjcnjsd
force*time= mass*vfinal
solve for vfinal
finalKE=1/2 m vf^2
To find the final kinetic energy of the ball after 12 seconds, we need to determine its final velocity first.
We can use Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum. Mathematically, this can be expressed as:
Force = mass × acceleration
Rearranging the formula to solve for acceleration:
acceleration = Force / mass
Substituting the given values:
acceleration = 21 N / 3 kg = 7 m/s^2
Next, we can use one of the kinematic equations that relates displacement, initial velocity, final velocity, acceleration, and time:
final velocity = initial velocity + (acceleration × time)
Since the ball starts from rest (initial velocity = 0), the equation simplifies to:
final velocity = acceleration × time
Substituting the given values:
final velocity = 7 m/s^2 × 12 s = 84 m/s
Finally, we can calculate the final kinetic energy of the ball using the formula:
kinetic energy = (1/2) × mass × (velocity)^2
Plugging in the values:
kinetic energy = (1/2) × 3 kg × (84 m/s)^2 = 2,520 J
Therefore, the final kinetic energy of the ball after 12 seconds is 2,520 Joules.