Category: Motion Along a Straight Line

In many types of motion, the acceleration is either constant or approximately so. For example, you might accelerate a car at an approximately constant rate when a traffic light turns from red to green. Then graphs of your position, velocity, and acceleration would resemble those in Fig. 2-8. (Note that a(t) in Fig. 2-8c is constant, which requires that ν(t)…

When a particle’s velocity changes, the particle is said to undergo acceleration (or to accelerate). For motion along an axis, the average acceleration aavg over a time interval Δt is where the particle has velocity ν1 at time t1 and then velocity ν2 at time t2. The instantaneous acceleration (or simply acceleration) is the derivative of the velocity with respect to time: In words, the acceleration of a particle at any…

You have now seen two ways to describe how fast something moves: average velocity and average speed, both of which are measured over a time interval Δt. However, the phrase “how fast” more commonly refers to how fast a particle is moving at a given instant—its instantaneous velocity (or simply velocity) ν. The velocity at any instant is obtained…

A compact way to describe position is with a graph of position x plotted as a function of time t—a graph of x(t). (The notation x(t) represents a function x of t, not the product x times t.) As a simple example, Fig. 2-2 shows the position function x(t) for a stationary armadillo (which we treat as a particle) over a 7 s time interval. The animal’s position stays…

To locate an object means to find its position relative to some reference point, often the origin (or zero point) of an axis such as the x axis in Fig. 2-1. The positive direction of the axis is in the direction of increasing numbers (coordinates), which is to the right in Fig. 2-1. The opposite is the negative direction. For example, a particle might…

The world, and everything in it, moves. Even seemingly stationary things, such as a roadway, move with Earth’s rotation, Earth’s orbit around the Sun, the Sun’s orbit around the center of the Milky Way galaxy, and that galaxy’s migration relative to other galaxies. The classification and comparison of motions (called kinematics) is often challenging. What exactly…

One purpose of physics is to study the motion of objects—how fast they move, for example, and how far they move in a given amount of time. NASCAR engineers are fanatical about this aspect of physics as they determine the performance of their cars before and during a race. Geologists use this physics to measure…