In which scenario would the kinetic energy of a moving object increase?
A.) Its speed doubles while its mass remains constant.
B.) Another object with an equal mass collides elastically with the moving object.
C.) A constant force is applied for twice the amount of time initially applied.
D.) An equal force acts in the direction opposite the object's motion for twice the distance originally traveled.
The correct answer would be A.) Its speed doubles while its mass remains constant.
The kinetic energy of an object is directly proportional to its mass and the square of its velocity, as given by the equation: KE = 0.5 * m * v^2, where KE represents kinetic energy, m represents mass, and v represents velocity (speed).
In option A, as the object's speed doubles while the mass remains constant, the velocity term (v^2) in the equation increases by a factor of 4 (2^2), resulting in an overall increase in kinetic energy.
In options B, C, and D, there is no mention of the speed changing while keeping the mass constant, so the kinetic energy would not be expected to increase in those scenarios.
To determine which scenario would cause the kinetic energy of a moving object to increase, let's analyze each option:
A.) If an object's speed doubles while its mass remains constant, the kinetic energy will increase. Kinetic energy is directly proportional to the square of the speed. Therefore, doubling the speed will result in an increase in kinetic energy.
B.) When an object collides elastically with another object of equal mass, the total kinetic energy of both objects remains the same. Although there might be a transfer of kinetic energy between the two objects, the total kinetic energy before and after the collision remains constant. So, in this scenario, the kinetic energy of the moving object would likely remain constant instead of increasing.
C.) If a constant force is applied for twice the amount of time initially applied, this would increase the object's velocity. However, kinetic energy is dependent on the square of the velocity. Since only the velocity and not the velocity squared is affected, the kinetic energy of the object would not increase but rather remain the same.
D.) If an equal force acts in the direction opposite the object's motion for twice the distance originally traveled, work is done against the motion, thereby decreasing the object's kinetic energy. In this case, the kinetic energy would decrease instead of increasing.
Based on the analysis above, the correct answer is A.) Its speed doubles while its mass remains constant.