Give the derived SI units for each of the following quantities in base SI units: (a) acceleration = distance/time \(^{2},\) (b) force \(=\) mass \(\times\) acceleration, \((\mathrm{c})\) work \(=\) force \(\times\) distance, (d) \(\quad\) pressure \(=\) force/area, (e) \(\quad\) power \(=\) work/time, (f) velocity \(=\) distance/time, \((\mathrm{g})\) energy \(=\operatorname{mass} \times(\text { velocity })^{2}\).

When studying motion, the term acceleration is used to describe how quickly an object's velocity changes. To measure acceleration in the System International (SI) units, we use meters per second squared (\(\frac{m}{s^2}\)). This means that for every second, the velocity of the object is changing by a certain number of meters per second. Imagine you're in a car that's speeding up; the car's acceleration is the rate at which it's getting faster as you press down on the accelerator.
For a clearer understanding, consider an object that starts from rest and reaches a velocity of \(10 \ m/s\) after 5 seconds. The acceleration would be \(2 \ m/s^2\), signaling that the object's velocity increased by \(2 \ m/s\) every second over that period. This understanding is crucial because acceleration is a vector quantity that not only has magnitude but direction as well.

The concept of force is fundamental in physics and describes any interaction that, when unopposed, changes the motion of an object. Force in SI units is measured in newtons (\(N\)). A newton is defined as the force required to accelerate a one-kilogram mass by one meter per second squared (\(1 \ kg\cdot\frac{m}{s^2}\)).
Consider pushing a shopping cart; the effort you exert to set it in motion is the force. Illustrated in a more technical manner, if you apply \(1 \ N\) to \(1 \ kg\) mass, it will accelerate at \(1 \ m/s^2\). This is directly derived from Newton's second law of motion, fundamentally linking force, mass, and acceleration together. It’s important to visualize this as it helps comprehend how forces act on objects in everyday scenarios.

In physics, work is done when a force is applied to an object and the object moves. The SI unit of work is the joule (\(J\)), which is equal to one kilogram meter squared per second squared (\(kg\cdot\frac{m^2}{s^2}\)).
To visualize work, imagine pushing that same cart a certain distance; you're exerting force over a displacement, which means you're performing work on the cart. A single joule is the amount of work done when a force of \(1 \ N\) moves an object a distance of \(1 \ m\) in the direction of the force. Understanding work as a concept is integral because it lays the foundation for discussions about energy transfer and mechanical advantage.

Pressure is applied when you press your hand against a wall or when you inflate a tire, and it's the force per unit area exerted on an object's surface. In SI units, pressure is measured in pascals (\(Pa\)), with one pascal equating to one newton per square meter (\(\frac{N}{m^2}\) or \(\frac{kg}{m\cdot s^2}\)).
A practical example is checking the tire pressure in a vehicle. If the pressure is \(200,000 \ Pa\) or \(200 \ kPa\), it means that each square meter of the tire's interior is being pushed against the tire walls with a force of \(200,000 \ N\). Understanding pressure is crucial for various fields including meteorology, engineering, and even medicine, where blood pressure is a vital health metric.

Power is a measure of how quickly work is done or energy is transferred. In SI units, power is measured in watts (\(W\)), where one watt equals one joule per second (\(\frac{J}{s}\) or \(kg\cdot\frac{m^2}{s^3}\)).
Imagine using a drill; the faster it spins and drills into a surface, the more power it is using. An electrical appliance rated at \(1 \ kW\) (1000 watts), for instance, uses \(1,000 \ J\) of energy per second when operating. Being able to compare power levels is useful not only in physics but in everyday life, as it helps people understand their energy consumption and efficiency.

Velocity is the speed of something in a given direction. It is a vector quantity, which means it includes both magnitude (how fast) and direction. In SI units, velocity is expressed in meters per second (\(m/s\)).
An example would be a train traveling north at \(90 \ m/s\); this statement provides both the speed of the train and its direction, defining its velocity. Clearly distinguishing between speed and velocity is crucial for understanding motion fully because it reveals not only how fast an object is moving but also where it's headed.

Energy is the capacity to do work or cause change; it comes in many forms such as kinetic, potential, thermal, and others. The SI unit for energy is the same as for work, the joule (\(J\)), signifying that energy is directly related to the concepts of work and power.
For example, a flying bird uses its kinetic energy to stay aloft, energy derived from the work of its muscles and the food it consumes. Understanding energy is vital because it is conserved in all physical processes—a concept known as the law of conservation of energy, one of the most fundamental principles in physics.