The position of any object must be given with respect to some reference point. An object’s position is its directed distance from a reference point. Movement is said to have occurred when the position of an object with respect to a given reference point has changed.

This change in position of an object is often called its displacement. Displacement, then, is a vector quantity. Distance, or length, is a scalar. Click here to explore differences between distance and displacement. Click here to make calculations and here to check your understanding.

In one dimensional motion, the displacement direction is often given as positive, +, or negative, -. A displacement of +3.5 m implies movement of 3.5 m in the positive direction. A displacement of -3.5 m implies movement of 3.5 m in the negative direction. Positive and negative directions are chosen arbitrarily, but usually agree with standard mathematical conventions.

vav t d = vav = average velocity; The average velocity of an object is defined to be the ratio of its change in position to the time taken to change the position. d vav = t vav = average velocity; in units of m/s, mph, ft/s, km/hr, etc... d = change in position, or displacement; in units of m, in, ft, km, mi, etc... t = change in time; in units of s, min, hr, etc...

The “sign” of the velocity indicates the direction of movement. A positive sign indicates movement in the positive direction. A negative sign indicates movement in the negative direction.

Speed is the magnitude of velocity. It is a scalar and has no direction given with it. Average speed is the total distance traveled divided by the total time taken. Average velocity is the total displacement divided by the total time taken. Average speed and average velocity are generally not equivalent because total distance and total displacement are generally not the same. When would they have the same magnitudes?

Speed is the absolute value of velocity. It is always a positive value. If an object increases its speed while traveling in the negative direction, its velocity actually decreases. If an object decreases its speed while traveling in the negative direction, its velocity actually increases.

aav t v = aav = average acceleration; v = change in velocity; The average acceleration of an object is defined to be the ratio of its change in velocity to the time taken to change the velocity. v aav = t aav = average acceleration; in units of m/s/s, mph/s, ft/s/s, km/hr/s, etc... v = change in velocity; in units of m/s, in/s, ft/s, km/hr, mph, etc... t = change in time; in units of s, min, hr, etc...

The “sign” of the acceleration indicates whether the velocity is increasing or decreasing. A positive sign indicates that the velocity is increasing. It will also be an increase in speed if the object is traveling in the positive direction. It is a decrease in speed otherwise. A negative sign indicates that the velocity is decreasing. It will also be a decrease in speed if the object is traveling in the positive direction. It is an increase in speed otherwise.

It is important to note that information about an object’s acceleration tells us how the object’s velocity is changing. In order to know what this change in velocity is doing to the object’s speed, we must know the direction the object is traveling. As a rule, if the object’s velocity and acceleration are in the same direction (have the same sign), we can say that the object’s speed is increasing. If the velocity and acceleration are in opposite directions (have opposite signs), we know that the object’s speed is decreasing. What can we say about changes in speed and/or velocity if the acceleration is either increasing or decreasing?

vf = vi + at d = vavt vav = (vf + vi)/2 d = vit + 0.5at2 Constant vf = vi + at t = time d = displacement d = vavt vi = initial velocity vav = (vf + vi)/2 vav = average velocity d = vit + 0.5at2 a = acceleration vf2 = vi2 + 2ad vf = final velocity

You can learn more about distance, displacement, speed, velocity, relative velocity, and acceleration by clicking on these simulation links: link1, link2, link3, link4, link5

Position – Time Graphs Summarized the y-coordinate at any time gives the position of the object the slope of a position-time graph at any instant is the instantaneous velocity of the object horizontal graph segments indicate that the object is “at rest” graph segments moving upward imply movement in the positive direction graph segments moving downward imply movement in the negative straight line graph segments indicate constant speed curving graph segments indicate changing speed graph segments becoming steeper indicate an increase in speed graph segments becoming less steep indicate a decrease in speed a change of direction is indicated whenever the graph is concave upward or downward

Velocity – Time Graphs Summarized the y-coordinate at any time gives the velocity of the object the slope of a velocity-time graph is the acceleration of the object horizontal graph segments indicate that the object has constant velocity graph segments above the x-axis imply movement in the positive direction graph segments below the x-axis imply movement in the negative horizontal segments on the x-axis indicate no movement straight line graph segments indicate constant acceleration graph segments moving upward indicate an increase in velocity graph segments moving downward indicate a decrease in velocity a change of direction is indicated whenever the graph crosses the x- axis an increase in speed is indicated by graph segments moving away from the x-axis

Acceleration – Time Graphs Summarized the y-coordinate at any time gives the acceleration of the object horizontal graph segments indicate that the object has constant acceleration a horizontal graph segment on the x-axis indicates that the object has constant velocity (no acceleration) graph segments above the x-axis imply increasing velocities graph segments below the x-axis imply decreasing velocities no changes in direction may be inferred from these graphs At the introductory physics level, we typically only deal with constant acceleration situations, so acceleration graphs generally consist of horizontal segments only.