A mechanic pushes a(n) 3980 kg car from

rest to a speed of v, doing 5107 J of work in
the process. During this time, the car moves
29.3m. Neglect friction between car and road.
Find the speed v.
Answer in units of m/s.

To find the speed v of the car, 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.

First, let's calculate the initial and final kinetic energies of the car:
Initial kinetic energy (K₁) = 0 (since the car is at rest)
Final kinetic energy (K₂) = (1/2)mv², where m is the mass of the car and v is the speed we want to find.

The work done on the car is given as 5107 J.

According to the work-energy principle:
Work done on the car (W) = K₂ - K₁

Substituting the values, we get:
5107 J = (1/2)(3980 kg)v² - 0

Now, let's solve for v:

(1/2)(3980 kg)v² = 5107 J
Multiplying both sides by 2:
(3980 kg)v² = 10214 J
Dividing both sides by 3980 kg:
v² = 10214 J / 3980 kg
v² ≈ 2.57 J/kg

To find the speed v, we need to take the square root of both sides:
v ≈ √(2.57 J/kg)

Calculating the square root:
v ≈ 1.60 m/s

Therefore, the speed of the car, neglecting friction between the car and the road, is approximately 1.60 m/s.