Question

F the mass of both vehicles were doubled, how would the final velocity and the change in kinetic energy be affected? (Select all that apply.)
The final velocities would each be 1/2 times as large in magnitude.
The final velocities would each have the same magnitude as before.
The final velocities would each be 2 times as large in magnitude.
The change in kinetic energy would be 2 times as great.
The change in kinetic energy would be half as great.
The change in kinetic energy would be unchanged.

Answer 1

Answer:

a) True. Speeds are reduced by half .  

e) True. kinety energy  is reduced by half

Explanation:

In order to analyze the statements you have we have to raise the problem solution.

If we fear a constant force when double the mass we can see the result in acceleration with Newton's second law

    F = m a₁

    F = (2m) a₂

    m a1 = 2m a₂

    a₂ = ½ a₁

We see that when I double the mass the acceleration is reduced by half

With kinematics we see that there is a linear relationship between speed and acceleration

    $v_{f}$ = v₀ + at

For the same initial speed and the same time if the acceleration is reduced by half the speed is reduced by half.

Therefore, by doubling the mass the speed reduces by half

kinetic energy is

     K = ½ m v²

     K = ½ (2m) (v/2)²

     K = (½ m v²) /2

     K = Ko / 2

Now we can review the claims

a) True. Speeds are reduced by half

b) False. We saw that they change their value

c) False. They reduce not increase

d) False. We saw that the kinetic energy is reduced

e) True. It is reduced by half

f) False. We saw that change