A mechanic pushes a 3090 kg car from rest
to a speed of v, doing 5497 J of work in the
process. During this time, the car moves
22.1 m.
Find the speed v. Neglect friction between
car and road.
Answer in units of m/s.
1/2mv^2 doesnt work
work = force * distance
f = 5497 / 22.1
a = f / m = 5497 / (22.1 * 3090)
d = 1/2 a t^2
... t = √(2d / a)
v = a t
To find the speed of the car, we can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy. In this case, the work done on the car is 5497 J.
The formula for work done on an object is given by:
Work = Change in Kinetic Energy
Since the car starts from rest, its initial kinetic energy is zero. So, the work done on the car is equal to its final kinetic energy:
5497 J = (1/2) * m * v^2
Where:
m = mass of the car = 3090 kg
v = final velocity of the car (speed)
Now, let's rearrange the equation to solve for v:
v^2 = (2 * Work) / m
Substituting the given values:
v^2 = (2 * 5497) / 3090
v^2 ≈ 3.64
Taking the square root of both sides:
v ≈ √3.64
v ≈ 1.91 m/s
Therefore, the speed of the car is approximately 1.91 m/s.
To find the speed of the car (v), we need to use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The equation for work done is given as:
Work = Change in Kinetic Energy
In this case, the work done by the mechanic is 5497 J, and since the car starts from rest, its initial kinetic energy is zero. Therefore, the equation becomes:
5497 J = Final Kinetic Energy - Initial Kinetic Energy
Since the car starts from rest, the initial kinetic energy is zero. Therefore, the equation simplifies to:
5497 J = Final Kinetic Energy
Now, the formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
Substituting the given values, the equation becomes:
5497 J = (1/2) * 3090 kg * v^2
Now we can solve for v:
5497 J = 1545 kg * v^2
Dividing both sides of the equation by 1545 kg:
3.5619 ≈ v^2
Taking the square root of both sides:
v ≈ √3.5619
v ≈ 1.88 m/s
Therefore, the speed of the car, neglecting the friction between the car and road, is approximately 1.88 m/s.