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a 2.0*10^3 kg car accelerates from rest under the actions of two forces. One is a forward force of 1140 N provided by traction between the wheels and the road. The other is a 950 N resistive force due to various frictional forces. Use the work-kinetic energy theorem to determine how far the car must travel for its speed to reach 2.0m/s?

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KE = 1/2mv^2 = (1/2)(2000)(2^2) = 4000 J This must equal the net work acting on the car. W=Fd The net force is 1140-950= 190N. so, d=W/F = 4000/190 = 21.05 m
Lanuel

The distance the car must travel for its speed to reach 2.0 m/s is 21.05 meters.

Given the following data:

  • Mass of car = [tex]2.0 \times 10^3[/tex] kg
  • Initial speed = 0 m/s (since the car accelerates from rest).
  • Forward force = 1140 Newton.
  • Resistive force = 950 Newton.
  • Final speed = 2 m/s.

To determine how far (distance) the car must travel for its speed to reach 2.0 m/s:

First of all, we would determine the kinetic energy possessed by the car.

Mathematically, kinetic energy is calculated by using the formula;

[tex]K.E = \frac{1}{2} MV^2[/tex]

Where:

  • K.E is the kinetic energy.
  • M is the mass of an object.
  • V is the velocity of an object.

Substituting the given parameters into the formula, we have;

[tex]K.E = \frac{1}{2} \times 2.0 \times 10^3 \times 2^2\\\\K.E = 1.0 \times 10^3 \times 4[/tex]

Kinetic energy = 4000 Joules.

The above kinetic energy possessed by the car is equal to the work done by the car.

  • Kinetic energy = work done = 4000 Joules.

Next, we would solve for the net force acting on the car:

[tex]Net\;force = Forward\;force - Resistive\;force\\\\Net\;force = 1140 - 950[/tex]

Net force = 190 Newton.

By applying the work-kinetic energy theorem, we would determine the distance travelled by the car;

[tex]Work \; done = Net\;force \times distance\\\\4000 = 190 \times distance\\\\Distance = \frac{4000}{190}[/tex]

Distance = 21.05 meters.

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