A 1,200 kg car initially traveling at 20 meters/second increases its speed to 28 meters/second. How much work did the car's engine have to do to cause this change?
A. 38,400 Joules
B. 230,400 Joules
C. 240,000 Joules
D. 470,400 Joules
(Show work will ya doll, please?)
To calculate the work done by the car's engine, we need to use the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.
The formula for work is given by the equation:
Work = F * d * cos(theta)
In this case, the car's engine provides the force required to accelerate the car. The displacement, d, is not given, but we can assume it to be a straight line given the scenario. Additionally, theta represents the angle between the force and displacement vectors, which we can assume to be zero since the force and displacement are in the same direction.
The work done is equal to the change in kinetic energy, which can be calculated using the formula:
Change in kinetic energy = (1/2) * m * (vf^2 - vi^2)
Where:
m = mass of the car = 1,200 kg
vi = initial velocity = 20 m/s
vf = final velocity = 28 m/s
Now, let's calculate the change in kinetic energy first:
Change in kinetic energy = (1/2) * 1,200 kg * ((28 m/s)^2 - (20 m/s)^2)
= (1/2) * 1,200 kg * (784 m^2/s^2 - 400 m^2/s^2)
= (1/2) * 1,200 kg * 384 m^2/s^2
= 230,400 kg m^2/s^2
= 230,400 Joules
Therefore, the work done by the car's engine to cause this change is 230,400 Joules.
So, the correct answer is B. 230,400 Joules.