A trailer mechanic pushes a 2500 kg car, home to a speed v, performing a job during the 5000 J. In this process, the car moves 25 m. Neglecting friction between the car and roadway:

(A) What is the final velocity v of the car?
(B) What horizontal force exerted on the car?

A) 1/2mv^2 - 1/2 mv^2= work

The first is the final KE
The second is the initial KE which = 0 since it was at rest

A trailer mechanic pushes a 2500 kg car, home to a speed v, performing a job during the 5000 J. In this process, the car moves 25 m. Neglecting friction between the car and roadway:

(A) What is the final velocity v of the car?
(B) What horizontal force exerted on the car?

To solve this problem, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.

Given:
Mass of the car (m) = 2500 kg
Work done (W) = 5000 J
Distance moved (d) = 25 m

(A) Final velocity (v):
To find the final velocity of the car, we need to calculate the change in kinetic energy.
Initial kinetic energy (K₁) = 0 (assuming the car was initially at rest)
Final kinetic energy (K₂) = 1/2 * m * v²

According to the work-energy principle, the work done on the car is equal to the change in its kinetic energy:
W = K₂ - K₁

Substituting the values:
5000 J = (1/2) * 2500 kg * v²

Simplifying the equation:
v² = (2 * 5000 J) / 2500 kg
v² = 4 m²/s²

Taking the square root of both sides:
v = √(4 m²/s²)
v = 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 force (F) is equal to mass (m) multiplied by acceleration (a).

The acceleration of the car (a) can be calculated using the final velocity (v) and distance (d) moved:
v² = u² + 2ad

Since the car starts from rest (u = 0), the equation becomes:
v² = 2ad

Substituting the given values:
(2 m/s)² = 2a * 25 m

Simplifying the equation:
4 m²/s² = 50a

Solving for acceleration (a):
a = 4 m²/s² / 50
a = 0.08 m/s²

Now, we can calculate the force (F) using Newton's second law:
F = m * a
F = 2500 kg * 0.08 m/s²
F = 200 N

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

To find the final velocity (v) of the car, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.

We are given the work done (W) on the car, which is 5000 J. We are also given the mass of the car (m), which is 2500 kg. The initial velocity (u) of the car is zero since it is at rest.

The work done on the car can be calculated using the equation:

W = (1/2) * m * (v^2 - u^2)

Since the initial velocity (u) is zero, the equation simplifies to:

W = (1/2) * m * v^2

Substituting the given values, we get:

5000 J = (1/2) * 2500 kg * v^2

Now, we can solve this equation to find the value of v. Rearranging the equation:

v^2 = (2 * 5000 J) / (2500 kg)
v^2 = 4 m^2/s^2

Taking the square root on both sides:

v = 2 m/s

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

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 the mass of the object multiplied by its acceleration.

In this case, the acceleration (a) can be calculated using the equation:

a = (v - u) / t

We are given the initial velocity (u) as zero, the final velocity (v) as 2 m/s, and the distance (d) covered by the car as 25 m.

Substituting the values, we get:

a = (2 m/s - 0 m/s) / (25 m)
a = 2 m/s^2

Now, we can find the force (F) exerted on the car using the equation:

F = m * a

Substituting the values, we get:

F = 2500 kg * 2 m/s^2

F = 5000 N

Therefore, the horizontal force exerted on the car is 5000 N.