suppose an automobile has a kinetic energy of 2900J. when it moves with 3 times the speed, what will be its kinetic energy?
answer in the units of joules
To find the kinetic energy of the automobile when it moves with 3 times the speed, we need to use the formula for kinetic energy:
Kinetic Energy = 1/2 * mass * velocity^2
Since the mass of the automobile remains constant, we can focus on the change in velocity.
Let's assume the initial velocity of the automobile is v. In this case, the initial kinetic energy will be:
Kinetic Energy₁ = 1/2 * mass * v^2 (Equation 1)
Now, the automobile moves with 3 times the speed, which means the new velocity will be 3v. The final kinetic energy can be calculated as:
Kinetic Energy₂ = 1/2 * mass * (3v)^2 (Equation 2)
To find the relation between the initial and final kinetic energies, we divide Equation 2 by Equation 1:
Kinetic Energy₂ / Kinetic Energy₁ = (1/2 * mass * (3v)^2) / (1/2 * mass * v^2)
Mass and 1/2 cancel out on both sides, leaving us with:
Kinetic Energy₂ / Kinetic Energy₁ = (9v^2) / (v^2) = 9
Therefore, the final kinetic energy is 9 times the initial kinetic energy:
Kinetic Energy₂ = 9 * Kinetic Energy₁
Substituting the given value of the initial kinetic energy (2900 J):
Kinetic Energy₂ = 9 * 2900 J = 26100 J
Hence, the kinetic energy of the automobile, when it moves with 3 times the speed, will be 26100 joules.