A mechanic pushes a 2.60 103-kg car from rest to a speed of v, doing 4,600 J of work in the process. During this time, the car moves 24.0 m. Neglecting friction between car and road, find each of the following.
To solve this problem, we need to use the work-energy principle. The principle states that the work done on an object is equal to the change in its kinetic energy.
Let's begin by identifying the given information:
- Mass of the car (m): 2.60 * 10^3 kg
- Work done on the car (W): 4,600 J
- Displacement of the car (s): 24.0 m
We want to find the final velocity (v) of the car. This can be done by applying the work-energy principle.
The work done on the car is given by the equation:
W = ΔKE
Since the car starts from rest, its initial kinetic energy (KE_i) is zero. Therefore, the equation becomes:
W = KE_f - KE_i
Rearranging the equation, we get:
KE_f = W
The equation for kinetic energy is given by:
KE = (1/2) * m * v^2
Substituting the values, we have:
(1/2) * m * v^2 = W
Plugging in the values:
(1/2) * 2.60 * 10^3 kg * v^2 = 4,600 J
Simplifying the equation:
v^2 = (2 * 4,600 J) / (2.60 * 10^3 kg)
v^2 = (9,200 J) / (2.60 * 10^3 kg)
v^2 = 3.53846153846 m^2/s^2
Taking the square root of both sides:
v = √(3.53846153846 m^2/s^2)
v ≈ 1.88 m/s
So, the final velocity of the car is approximately 1.88 m/s.