A 2.84 × 103 kg car requires 5.4 kJ of work to move from rest to some final speed. During this time, the car moves 20.4 m.
Neglecting friction, find a) the final speed.
KE = M*V^2/2
KE = 5400 J.
M = 2840 kg
Solve for V. Units: 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 given as 5.4 kJ (or 5.4 × 10^3 J), and we want to find the final speed of the car.
The equation for the work done on an object is:
Work = Change in Kinetic Energy
Since the car starts from rest, its initial kinetic energy is zero. So the equation becomes:
5.4 × 10^3 J = (1/2) × m × v^2
where m is the mass of the car and v is the final velocity.
The mass of the car is given as 2.84 × 10^3 kg.
Plugging in the values, the equation becomes:
5.4 × 10^3 J = (1/2) × (2.84 × 10^3 kg) × v^2
Simplifying the equation, we get:
v^2 = (2 × 5.4 × 10^3 J) / (2.84 × 10^3 kg)
v^2 = 5.4 × 10^3 J / 2.84 × 10^3 kg
v^2 = 1.901 × 10^3 m^2/s^2
Taking the square root of both sides, we get:
v ≈ 43.61 m/s
Therefore, the final speed of the car is approximately 43.61 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. To use this value in our calculation, we need to convert it to joules. Since 1 kJ = 1000 J, we can multiply 5.4 kJ by 1000 to get the work done in joules:
5.4 kJ * 1000 J/kJ = 5400 J
The change in kinetic energy is equal to the final kinetic energy of the car minus its initial kinetic energy. Since the car starts from rest, its initial kinetic energy is zero.
Therefore, we have:
Change in kinetic energy = final kinetic energy - initial kinetic energy
Change in kinetic energy = (1/2) * mass * (final speed^2) - 0
Since the mass of the car is given as 2.84 × 10^3 kg and the change in kinetic energy is given as 5400 J, we can substitute these values into the equation:
5400 J = (1/2) * (2.84 × 10^3 kg) * (final speed^2)
We can then rearrange the equation to solve for the final speed:
(final speed^2) = (2 * 5400 J) / (2.84 × 10^3 kg)
(final speed^2) = 10800 J / (2.84 × 10^3 kg)
(final speed^2) = 3.802 kg·m^2·s^-2 / 2.84 × 10^3 kg
(final speed^2) = 3.802 / (2.84 × 10^3) m^2·s^-2·kg^-1
(final speed^2) = 1.337 m^2·s^-2·kg^-1
Taking the square root of both sides of the equation, we can find the final speed:
final speed = √(1.337 m^2·s^-2·kg^-1)
Calculating this value gives us the final speed of the car.