A mechanic pushes a 2,500 kg car from rest to a speed v, with 5000J of work. During this process the car moves 25m. Neglecting friction, calculate: a) the final velocity of car b) The horizontal force exerted on the car

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To solve this problem, we first need to understand the relationship between work, force, and distance.

The work done on an object is equal to the force applied multiplied by the distance over which the force is exerted. Mathematically, this can be expressed as:

Work = Force * Distance

In this case, we are given the work done, which is 5000 J, and the distance moved by the car, which is 25 m. We need to determine the force exerted on the car, as well as the final velocity.

a) Final Velocity of the Car:
To find the final velocity of the car, we can use the work-energy principle, which states that the net work done on an object is equal to its change in kinetic energy. Mathematically, this can be expressed as:

Work = ΔKE

Where ΔKE represents the change in kinetic energy of the object.

The initial kinetic energy of the car is zero, as it starts from rest. Therefore, the work done on the car by the mechanic is solely responsible for its final kinetic energy.

So, we can write the equation as:

5000 J = (1/2) * mass * (final velocity)^2

Rearranging the equation to solve for the final velocity:

final velocity = √((2 * work) / mass)

Plugging in the given values:

final velocity = √((2 * 5000 J) / 2500 kg)

final velocity = √((10000 J) / 2500 kg)

final velocity = √(4 J/kg)

final velocity = 2 m/s

Therefore, the final velocity of the car is 2 m/s.

b) Horizontal Force Exerted on the Car:
To find the horizontal force exerted on the car, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. Mathematically, this can be expressed as:

Force = mass * acceleration

In this case, we need to find the force exerted on the car to accelerate it horizontally.

The work done on the car is equal to the force multiplied by the distance. Therefore, we can write:

Work = Force * Distance

Rearranging the equation to solve for the force:

Force = Work / Distance

Plugging in the given values:

Force = 5000 J / 25 m

Force = 200 N

Therefore, the horizontal force exerted on the car is 200 N.