A 2.38 × 103 kg car requires 5.4 kJ of work to
move from rest to some final speed. During
this time, the car moves 28.1 m.
Neglecting friction, find
a) the final speed.
Answer in units of m/s.
To find the final speed of the car, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The work done on the car is given as 5.4 kJ (kilojoules), which is equivalent to 5400 J (joules).
The change in kinetic energy is equal to 1/2 * mass * final velocity^2.
We can set up the equation as follows:
Work = Change in Kinetic Energy
5400 J = 1/2 * mass * final velocity^2
The mass of the car is given as 2.38 × 10^3 kg.
Substituting these values into the equation, we get:
5400 J = 1/2 * (2.38 × 10^3 kg) * final velocity^2
Simplifying the equation:
10800 = (2.38 × 10^3) * final velocity^2
Dividing both sides by (2.38 × 10^3), we get:
final velocity^2 = 10800 / (2.38 × 10^3)
final velocity^2 = 4.5378
Taking the square root of both sides, we get:
final velocity ≈ 2.13 m/s
Therefore, the final speed of the car is approximately 2.13 m/s.
To find the final speed of the car, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the car is the amount of work required to move it from rest to the final speed.
The work done on an object can be calculated using the formula:
Work = Force x Distance x cos(θ)
In this case, we don't have information about the force or the angle, but we are given the work (5.4 kJ) and the distance (28.1 m). We need to convert the work from kilojoules (kJ) to joules (J) since the SI unit for work is Joules.
1 kJ = 1000 J
So, the work done on the car is:
Work = 5.4 kJ x 1000 J/kJ = 5400 J
Now, since the car is initially at rest, the initial kinetic energy is zero. Therefore, the total work done on the car is equal to its final kinetic energy.
Work = Final Kinetic Energy
The kinetic energy of an object can be calculated using the formula:
Kinetic Energy = (1/2) x mass x velocity^2
In this case, we need to solve for the final velocity (speed). Rearranging the formula, we get:
Final Velocity^2 = (2 x Work) / Mass
Inserting the given values, we have:
Final Velocity^2 = (2 x 5400 J) / 2.38 x 10^3 kg
Calculating this expression, we find:
Final Velocity^2 = 2281.512 J / 2.38 x 10^3 kg
Final Velocity^2 = 957.961 J/kg
Taking the square root of both sides, we get:
Final Velocity = √(957.961 J/kg)
Evaluating this expression, we find:
Final Velocity = 30.982 m/s
Therefore, the final speed of the car is approximately 30.982 m/s.