AP Physics ReviewKinematics

Terms

Distance – the total measured path that an object travels. (scalar)

Displacement – the measured straight line distance from when the object starts to where it ends. (vector, watch for negatives)

Speed – distance traveled divided by total time of travel or rate of change of position (scalar)

Velocity – Displacement divided by total time or rate of change of displacement. (vector, watch for negatives)

Acceleration – rate of change of velocity (vector, + increasing velocity, negative decreasing velocity in horizontal motion)

Ave vs. Instantaneous

Average velocity is the total displacement divided by total time. There could be many different velocities that occur during the trip that are not equal to the ave velocity.

Instantaneous velocity is the exact velocity at a particular moment. This can be found as the change in time approaches 0. The smaller the time interval the more accurate the inst velocity.

Ave velocity can also be found with:

This assumes that each velocity was maintained for an equal amount of time.

Graphing Motion

Slope of a position time graph = velocity Slope of a velocity time graph =

acceleration Area under acceleration time graph =

ave. velocity Area under velocity time graph =

displacement.

Cont’d

Analyze the slope as being positive or negative since all of the these are vectors.

For curved lines, the change in the slope (tangent line) gives you a clue to the motion of the object too.

Keep in mind, we do not deal with changing accelerations. Therefore we will not see any slope on an acceleration vs time graph.

Basic Equations

The left side deals with horizontal motion and the right side deals with vertical motion.

Common strategies:-List your known variables and the variable you are looking to find.-Look for an equation that includes of those variables.-If one does not exist, can you solve for a different unknown that will help?-Can you solve an equation for an unknown and substitute it in to another equation?

Vertical Motion

Use the equations below. Acceleration will most likely be

acceleration due to gravity -9.8m/s2

If an object is falling its velocity is negative and so is the displacement.

Horizontal Projectiles

vx is constant during the entire parabolic path.

Initial vertical velocity is 0 and increase due to g.

Use kinematics equations to solve. Time for an object drop from

height y is equal to the time for an object to hit the ground when launched horizontally from height y.

You can solve for time in terms of horizontal and vertical displacements and set them equal to each other.

Only height affects launch time, not horizontal v.

Projectiles @ an Angle

First step is to find the vertical and horizontal components of the original launch v. Launch v will not be used again.

Horizontal v stays constant. Vertical v decreases(but +) on the way up, is zero at the top of the path and increases(but -) on the way down.

For t, we know final vertical v at the top is 0. solve for time to that point and then t up = t down.

When dealing with vertical unknowns such as max height. We always go to the peak of the path.

Range = horizontal v x total time. Max range when angle = 45 Max time in air when angle = 90 2 angles equidistant fro 45 degrees will have

the same range. Ie. 10 and 80 or 30 and 60.

UCM Centripetal force and centripetal

acceleration are directed toward the center of the path.

Centripetal force is not a real force and should therefore not be labeled on an FBD, it must be caused by something. EX gravity, friction etc.

Velocity is directed tangentially to the path of motion as shown in the diagram.

The “force” direction away from the center of the path is due to the inertia of the object wanting to continue in a straight line.

Chase Problems

In many problems, two objects are either approaching each other, chasing each other, or trying to get away from each other. Some examples might be: a police car chasing a speeding car, a passenger chasing a departing train or bus, an ambulance moving through traffic, two cars moving through an intersection, two vehicles coming towards each other on a two-line road, or two one-dimensional projectiles traveling in the same or opposite directions while moving through the air.

xpursuer = "gap" + xleader vot + ½at2 number vot + ½at2

vt   vt

Each column in the above table states the allowed behaviors for the pursuer and the leader. Each participant can either be experiencing accelerated or linear motion. The numerical value of the "gap" can be equal to zero (if the two objects start side-by-side) or it can be a nonzero number. The parameter t, for time, unites the equations. To solve chase equations, you first determine the time that is required for the two objects to come together - then, you use that time to determine the position of their collision.

To work this type of problem, one object is considered the leader and the other is the pursuer. The pursuer, in reaching the leader's final location, must not only close the leader's original gap but also account for any subsequent displacement the leader travels while being chased.

In a swimming race, a father gives his 4 year old son a 10-second head-start. The pool is 25-meters long. The child swims at 0.80 m/sec while the father swims at 1.20 m/sec. How far is the child ahead of the father when

the father gets to start swimming? What chase equation must you solve to

determine the winner? At what time does the father come up alongside

his son? How far has the father swum at that point? Who wins the race? Describe the s-t graph for this problem.

How far is the child ahead of the father when the father gets to start swimming?  

x = vtx = (0.8)(10)x = 8 meters

What chase equation must you solve to determine the winner?  

1.20m/s t = 8m + 0.8m/s t

At what time does the father come up alongside his son?  

1.2m/s t = 8m + 0.80m/s t0.4m/s t = 8m

t = 20 seconds

How far has the father swum at that point?  

x = vtx = (1.20m/s)(20s)x = 24 meters

Who wins the race?   The father out touches his son by 0.42 seconds.

  There is one meter left to swim when the father

comes up alongside his son. The father will travel that meter in 1 m / 1.2 m/sec = 0.833 second. The son will travel that final meter in 1 m / 0.8 m/sec = 1.25 seconds. Subtracting we find that the father will win by 0.42 seconds.

The father wins the race and “Father of The Year” for beating his 4 year old son.

Describe the s-t graph for this problem.