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In this section, we will delve into and review some ideas about motion, force, and energy.
Force and motion are intimately intertwined concepts because a force is required to change an object’s motion. To get anywhere in understanding concepts in motion, you must first understand the terminology. Be careful here. As is typical in science, familiar words are used with very specific meanings that are different from their everyday meanings. Don’t assume that because a word is familiar that you know its meaning in this context.
Speed and velocity are not the same thing even though they are often used as interchangeable terms. The basic difference is that velocity includes the direction of motion while speed does not. When you are driving, the speed of your car might be 50 miles per hour; its velocity might be 50 miles per hour towards the east. If in the same situation we look at your velocity toward the north, the result is very different. The speed of the car is still 50 miles per hour, but your velocity is zero! The reason for this is that the direction part of the velocity is all toward the east and nothing is directed toward the north. Velocity requires both the magnitude AND a direction.
An acceleration is a change in the velocity over a period of time. Specifically, acceleration is defined as the time rate change of velocity (a = v/t). You may be used to thinking of accelerating as speeding up, but it also includes slowing down and changing direction. Like velocity, the acceleration is a vector quantity that also includes the direction. An acceleration perpendicular to the velocity will change the direction of the velocity without changing the speed.
Acceleration, velocity, and speed are all rates of change. Velocity and speed measure the rate at which the position changes, while acceleration measures the rate at which the velocity changes.
Hence the average speed over an interval is defined as the change in position, or displacement, during that time. If it takes you an hour to drive to a town 50 miles away, your average speed will be 50 miles per hour. If the town is east of your home, your average velocity will be 50 miles per hour towards the east.
The average acceleration is defined in a similar way. It is the change in velocity during a time interval divided by the time interval.
If a 2,500-mile cross country flight takes 5 hours, what is the average speed of the plane?
The correct answer is C, 500 miles per hour. The average speed is the distance divided by the time or 2,500 miles divided by 5 hours.
Both can be represented on a graph as the slope of a line. On a graph with time as the x-axis (horizontal) and position as the y-axis (vertical), a constant velocity will be represented by a straight line, and the slope will be the value of the velocity or speed. A steeper slope indicates a higher velocity. If the line is curved, then the velocity is changing. In a similar fashion, a graph with velocity as the y-axis and time as the x-axis will show the acceleration.
In order to have acceleration, there must be an unbalanced force applied to an object. This statement is the essential meaning of Newton’s first law. If there are no unbalanced forces acting on an object, that doesn’t mean the object is at rest. The object could be moving at a constant velocity. Macroscopic forces that we experience include gravity, friction, electromagnetic forces, and contact forces such as pushing on a surface.
Think about the following:
A box is sliding across the floor. When you stop pushing the box—applying a force—the box slows to a stop because
Friction is the key here.
Objects do not need to have force acting on them in order to keep moving. They only need the force to accelerate them (change their velocity). The frictional force of the floor accelerates the box in the direction opposite its velocity, so it slows to a stop.
Pressure is force divided by area. A sharp knife cuts food more easily than a dull one because with a sharp knife the same force is applied to a smaller area. Hence you can exert more pressure with a sharp knife than a dull one. We also feel pressure from air, water, and other fluids. This pressure increases with depth. So atmospheric pressure at sea level is greater than on a mountaintop. Similarly, when we dive to the bottom of a swimming pool, we feel a greater water pressure at a greater depth.