A 1300 kg car starts from rest at a stoplight and accelerates to a speed of 14 m/s over adisplacement of 82 m. T/I(a) Calculate the net work done on the car. [ans: 130 kJ](b) Calculate the net force acting on the car.
Question
A 1300 kg car starts from rest at a stoplight and accelerates to a speed of 14 m/s over adisplacement of 82 m. T/I(a) Calculate the net work done on the car. ans: 130 kJ Calculate the net force acting on the car.
Solution
(a) To calculate the net work done on the car, we can use the work-energy theorem which states that the work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy (Ki) of the car is 0 (since it starts from rest), and the final kinetic energy (Kf) can be calculated using the formula:
Kf = 1/2 * m * v^2
where m is the mass of the car (1300 kg) and v is the final speed (14 m/s).
So, Kf = 1/2 * 1300 kg * (14 m/s)^2 = 127400 J = 127.4 kJ
Therefore, the net work done on the car is equal to the change in kinetic energy, which is Kf - Ki = 127.4 kJ - 0 = 127.4 kJ. The answer is approximately 130 kJ when rounded to the nearest ten.
(b) To calculate the net force acting on the car, we can use the formula:
F = m * a
where m is the mass of the car (1300 kg) and a is the acceleration.
We can find the acceleration using the formula:
a = (v - u) / t
where v is the final velocity (14 m/s), u is the initial velocity (0 m/s), and t is the time. However, we don't have the time. But we can use another formula to find acceleration:
a = (v^2 - u^2) / (2 * s)
where s is the displacement (82 m).
So, a = ((14 m/s)^2 - (0 m/s)^2) / (2 * 82 m) = 1.19 m/s^2
Therefore, the net force acting on the car is F = 1300 kg * 1.19 m/s^2 = 1547 N.
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