An engineer is designing a small toy car that a spring will launch from rest along a racetrack. She wants to maximize the kinetic energy of the toy car when it launches from the end of a compressed spring onto the track, but she can make only a slight adjustment to the initial conditions of the car. The speed of the car just as it moves away from the spring onto the track is called the launch speed. Which of the following modifications to the car design would have the greatest effect on increasing the kinetic energy of the car? Explain your reasoning.
Decrease the mass of the car slightly.
Increase the mass of the car slightly.
Decrease the launch speed of the car slightly.
Increase the launch speed of the car slightly.

we see that to increase the energy of the expensive we must increase the launch speed, since it increases quadratically

Explanation:

Kinetic energy is

            K = ½ m v²

the speed of the expensive we can find it r

            v² = v₀² + 2 a x

we can find acceleration with Newton's second law

            F = m a

             a = F / m

             F= cte

substitute in the velocity equation

           v² = v₀² + 2 F/m  x

let's substitute in the kinetic energize equation

         K = ½ m (v₀² + 2 F/m  x)

         K = ½ m v₀²  + f x

we see that the kinetic energy depends on two tomines

in January in these systems the force for launching is constant, which is why decreasing the mass increases the speed of the vehicle and therefore increases the kinetic energy

As the launch speed increases the initial energy increases quadratically

we see that to increase the energy of the expensive we must increase the launch speed, since it increases quadratically