A mechanic pushes a 2520 kg car from rest
to a speed of
v
, doing 4310 J of work in the
process. During this time, the car moves
22.4 m.
Find the speed
v
. Neglect friction between
car and road. Answer in units of m/s.
change of momentum = 2520 v
average force = change of momentum/time
F = 2520 v/t
work = force * distance
4310 = 2520 v/t * 22.4
or
v/t = .0764 or t = v/.0764
now if force were constant
d = (1/2) a t^2
44.8 = a t^2
v = a t so a = v/t
so
44.8 = v t = v^2/.0764
v^2 = 3.42
v = 1.85 m/s
To find the speed of the car, we can use the work-energy principle. According to the principle, the work done on an object is equal to the change in its kinetic energy.
In this case, the work done by the mechanic on the car is 4310 J, and the car moves from rest to a certain speed. We can assume the initial kinetic energy of the car is zero since it starts from rest.
The work-energy principle can be expressed as:
Work = Change in Kinetic Energy
The change in kinetic energy can be calculated using the equation:
Change in Kinetic Energy = (1/2) * mass * (final velocity^2 - initial velocity^2)
Here, the mass of the car is 2520 kg and the initial velocity is 0, so the equation becomes:
Change in Kinetic Energy = (1/2) * 2520 kg * (v^2 - 0^2)
Since the work done on the car is equal to the change in kinetic energy, we can set up the equation:
Work = Change in Kinetic Energy
4310 J = (1/2) * 2520 kg * (v^2 - 0^2)
Now, we can solve for the speed v.
4310 J = (1/2) * 2520 kg * v^2
Divide both sides by (1/2) * 2520 kg:
4310 J / ((1/2) * 2520 kg) = v^2
2 * 4310 J / 2520 kg = v^2
Now, solve for v^2:
v^2 = (2 * 4310 J) / 2520 kg
v^2 = 8620 J / 2520 kg
v^2 ≈ 3.42 m^2/s^2
Finally, take the square root of both sides to find v:
v ≈ √(3.42 m^2/s^2)
v ≈ 1.85 m/s
Therefore, the speed of the car is approximately 1.85 m/s.
To find the speed of the car, we need to use the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
In this case, the work done on the car is given as 4310 J.
The change in kinetic energy of the car can be calculated using the formula:
ΔKE = KE_final - KE_initial
Since the car starts from rest, the initial kinetic energy (KE_initial) is zero.
The final kinetic energy (KE_final) can be calculated as:
KE_final = (1/2) * m * v^2
where m is the mass of the car and v is its speed.
Substituting the values given in the problem:
4310 J = (1/2) * 2520 kg * v^2
To find v, we need to solve the above equation for v.
First, divide both sides of the equation by (1/2) * 2520 kg:
4310 J / [(1/2) * 2520 kg] = v^2
Simplifying:
4310 J / 1260 kg = v^2
v^2 = 3.42 m^2/s^2
To find v, take the square root of both sides:
v = √(3.42 m^2/s^2)
Calculating the square root, we get:
v ≈ 1.85 m/s
So, the speed of the car is approximately 1.85 m/s.
easier way
work done = final (1/2) m v^2
4310 = (1/2)2520 v^2
v = 1.85 m/s ;)