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

3. Displacement, then, is a vector quantity. Distance, or length, is a scalar. Click here and here to explore differences between distance and displacement. here This change in position of an object is often called its displacement. It is the straight line distance and direction from the starting point to the ending point, regardless of the path taken.

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

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

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

7. Speed Speed is the magnitude of velocity. scalar It is a scalar and has no direction given with it. Average speedtotal distance Average speed is the total distance traveled divided bytotal time divided by the total time taken. Average velocitytotal displacement Average velocity is the total displacement divided bytotal time 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?

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

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

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

11. 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?

12. Constant v f = v i + at d = v av t v av = (v f + v i )/2 d = v i t + 0.5at 2 v f 2 = v i 2 + 2ad t = time d = displacement v i = initial velocity v av = average velocity a = acceleration v f = final velocity

13. You can learn more about distance, displacement, speed, velocity, relative velocity, and acceleration by exploring these links: link1link1, link2, link3 link2link3 link1link2link3

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

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

16. Acceleration – Time Graphs Summarized the y-coordinate at any time gives the acceleration of the object the y-coordinate at any time gives the acceleration of the object horizontal graph segments indicate that the object has constant horizontal graph segments indicate that the object has constant acceleration acceleration a horizontal graph segment on the x-axis indicates that the object a horizontal graph segment on the x-axis indicates that the object has constant velocity (no acceleration) has constant velocity (no acceleration) graph segments above the x-axis imply increasing velocities graph segments above the x-axis imply increasing velocities graph segments below the x-axis imply decreasing velocities graph segments below the x-axis imply decreasing velocities no changes in direction may be inferred from these graphs 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.