When you throw a ball, the work you do to accelerate it equals the kinetic energ

Question

When you throw a ball, the work you do to accelerate it equals the kinetic energy the ball gains. If you do twice as much work when throwing the ball, does it go twice as fast? Explain.

2 When you throw a ball, the work you do to accelerate it equals the kinetic energy the ball gains. If you do twice as much work when throwing the ball, does it go twice as fast? Explain. Yes. Twice as much work will give the ball twice as much kinetic energy. Since KE is proportional to the speed, the speed will double as well. Yes. Twice as much work will give the ball four times as much kinetic energy. Since KE is proportional to the speed squared, the speed will be the square root of 4, or twice as fast. No. Twice as much work will give the ball four times as much kinetic energy. Since KE is proportional to the speed, the speed will be four times larger. No. Twice as much work will give the ball twice as much kinetic energy. But since KE is proportional to the speed squared, the speed will be times larger

Explanation / Answer

Kinetic energy = 1/2 MV^2

Twice work = 1/2 M X^2 (X is the new velocity) = MV^2

Therefore the Velocity of the Twice work

1/2 MX^2 = MV^2 ,

X^2 = 2 V^2

X = sqrt(2) V

This means the new velocity X is sqrt (2) times greater than the initial velocity.

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