A1500 kg car accelerates from rest under the actions of two forces. One is a forward force of
1260 N provided by traction between the wheels and the road. The other is a 870 N resistive
force due to various frictional forces. Use the work-energy theorem to determine how far the
car must travel for its speed to reach 9.5 m/s.
I don't know how to set this up
net force=mass*acceleration
a=netforce/mass
and
vf^2=2ad=2d*(1260-870)/1500
solve for distance d
Ummm don't understand. Is this correct?
1/2[1500][9.5]=[1260-870]cos[d]
solve for d
d=1/2 *1500/(390)
solve for d
d=1/2 *1500*9.5^2/(390)
To use the work-energy theorem to determine the distance traveled by the car, we need to consider the net work done on the car. The net work is equal to the change in kinetic energy, which is given by the equation:
Net Work = Change in Kinetic Energy
The net work can be calculated as the sum of the work done by the forward force and the work done by the resistive force:
Net Work = Work by Forward Force + Work by Resistive Force
The work done by a force is equal to the magnitude of the force multiplied by the displacement of the object in the direction of the force:
Work = Force × Displacement
In this case, the forward force is acting in the direction of motion, so it contributes positively to the work done. The resistive force is acting in the opposite direction of motion, so it contributes negatively to the work done.
The displacement of the car can be denoted as "d". So we have:
Net Work = (Forward Force × d) + (Resistive Force × d)
Given that the forward force is 1260 N and the resistive force is 870 N, we can rewrite the equation as:
Net Work = (1260 N × d) + (-870 N × d)
Since the net work is equal to the change in kinetic energy, we can use the work-energy theorem:
Net Work = Change in Kinetic Energy
The change in kinetic energy can be calculated as the final kinetic energy minus the initial kinetic energy:
Change in Kinetic Energy = (1/2) × (Mass of the car) × (Final Velocity^2 - Initial Velocity^2)
In this case, the car is initially at rest (Initial Velocity = 0), and its mass is given as 1500 kg. The final velocity is 9.5 m/s. We can substitute these values into the equation:
Change in Kinetic Energy = (1/2) × 1500 kg × (9.5 m/s)^2
Now we can equate the Net Work and the Change in Kinetic Energy:
(1260 N × d) + (-870 N × d) = (1/2) × 1500 kg × (9.5 m/s)^2
Now all you need to do is solve this equation for the value of "d", which represents the distance traveled by the car.