91Ó°ÊÓ

Uniformly accelerated motion refers to a scenario where an object's velocity changes at a constant rate. Here, the acceleration is unchanging over time. In our car example, the vehicle starts from rest and reaches a velocity of 18.0 m/s over a 12.0 s period.

To calculate the acceleration, the formula used is:
\(a = \frac{v_f - v_i}{t}\)
where \(a\) is the acceleration, \(v_f\) is the final velocity, \(v_i\) is the initial velocity, and \(t\) is the time. For the car, as it starts from rest (\(v_i = 0\)), the calculation simplifies to: \(a = \frac{18.0\ m/s}{12.0\ s} = 1.5\ m/s^2\). This acceleration is uniform, meaning the car's velocity increases by 1.5 m/s every second.

The net force is the sum of all forces acting upon an object. It's vital for determining an object's acceleration according to Newton's second law, which states \(F_{net} = ma\), where \(F_{net}\) is the net force, \(m\) is the mass, and \(a\) is the acceleration.

For the car in our problem, air resistance, which works in the opposite direction of the car's motion, acts as a counteracting force and must be subtracted from the total force provided by the car's engine. The net force calculation can therefore be updated to include this resistant force: \(F_{net} = ma - F_{air}\).

Substituting in the mass of the car, its calculated acceleration, and the constant air resistance, we obtained the net force acting on the car to propel it forward.

The work-energy principle is a foundational concept in physics, expressing the relationship between the work done on an object and its energy. Work is defined as a force applied over a distance and is given by the formula \(W = F_{net} * d\), where \(W\) is the work, \(F_{net}\) is the net force, and \(d\) is the distance moved in the direction of the force.

In the car example, we needed to first find how far the car traveled during the acceleration period. Using the motion equation \(d = v_i*t + 0.5*a*t^2\), and then multiplying the net force by this distance to find the total work done. This concept links the forces acting on the car and the car's displacement to describe how much energy was transferred to accelerate the car.

Power in mechanics is a measure of how quickly work is done or energy is transmitted. The standard SI unit for power is the watt (W). Average power and instantaneous power are two key concepts here.

Average power \(P_{avg}\) is the total work divided by the time over which the work was performed: \(P_{avg} = \frac{W}{t}\). For our car, we calculated this by dividing the total work by the 12.0 s period. In contrast, instantaneous power \(P_{inst}\) is measured at a specific moment in time and can be found by multiplying the net force by the instantaneous velocity at that time: \(P_{inst} = F_{net} * v\).

In the final step of our exercise, we found the instantaneous power of the car at 12.0 s by using the net force at that moment and the car's velocity, providing us with the power output just as the car finished accelerating.