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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
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
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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