The engine of a racing car of mass m delivers a constant power P at full throttle. Assuming that the friction drag force on the car is proportional to the velocity: Fdrag = -cv where c is a positive constant.What maximum speed can be attained by the car on level ground?
To determine the maximum speed that can be attained by the car on level ground, we need to balance the engine power with the drag force acting against the car.
The power delivered by the engine is given as a constant P. Power is defined as the rate at which work is done or energy is transferred, and in this case, it is constant regardless of the car's speed.
The work done by the engine per unit time is equal to the power: P = Fengine * v, where Fengine is the force exerted by the engine and v is the velocity of the car.
Now, let's consider the drag force acting on the car. The drag force is given as Fdrag = -cv, where c is a positive constant. Since the drag force opposes the motion of the car, it is in the opposite direction of the velocity and has a negative sign.
When the car reaches its maximum speed, the drag force will be equal in magnitude but opposite in direction to the engine force. Therefore, we can set Fengine = -Fdrag:
Fengine = -Fdrag
=> Fengine = cv
Substituting the expression for the engine force into the power equation:
P = cv * v
To find the maximum speed, we need to solve for v. To do this, rearrange the equation:
v = P / c
Therefore, the maximum speed that can be attained by the car on level ground is given by v = P / c.