1. 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...

2. 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.

3. 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?

5. Constant Δx = v av t v av = (v i + v f )/2 v f = v i + at Δx=v i t + 0.5at 2 v f 2 = v i 2 + 2aΔx t = time elapsed Δx = displacement v i = initial velocity v av = average velocity a = acceleration v f = final velocity

6. 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

7. Position-Time Graphs

8. 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

10. 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.