2.1 Kinematics in One Dimension Mechanics – motion and the forces that cause that motion...

2.1 Kinematics in One Dimension

• Mechanics – motion and the forces that cause that motion

• Kinematics – describes motion without regard to the forces that cause that motion

• Dynamics – describes the forces that cause the motion

Displacement – change in position

Distance and displacement are NOT the same.

Note displacement needs a direction

2.2 Speed and Velocity (they are not the same either)

Average velocity and constant velocity

Example: The initial position of a runner is 50.0 m. 3.00 s later, the runner is at 30.0 m. What is the average velocity of the runner?

2.3 Acceleration (also known as “what’s a meter per second per

second?”)

A brief and simple, yet fundamentally important

comparison of velocity and acceleration.

Example: A car accelerates from rest to 75 km/h in 5.0 s. What is the average acceleration?

Example: During the time interval of 9.0 s to 14 s, a drag racer slows (using a parachute – or perhaps by dragging a comatose llama in a burlap bag) from 15.0 m/s to 5.0 m/s. What is the acceleration?

A few notes on signs and acceleration

• If acceleration and velocity have the same sign, the object is increasing in speed.

• If acceleration and velocity have opposite signs, the object is decreasing in speed.

A few light and humorous moments as Mr. Evans walks across the front of the room.

2.4 Kinematics equations for constant acceleration (The Big

Four)

Rewriting the equation for acceleration

An equation for displacement

Example: What is the maximum displacement required for a car moving at 28 m/s to come to a stop if the average acceleration is –6.0 m/s2?

A second equation for displacement

Wait a minute, I think I see another kinematics equation . . .

Ex. A race car starts from rest and accelerates at –5.00 m/s2. What is the velocity of the car after it has traveled –30.5 m?

Ex. A car travels at a constant speed of 30.0 m/s passing a trooper hidden behind a billboard. One second later, the trooper chases the car while accelerating at 3.00 m/s2. How long does it take for the trooper to overtake the car?

2.6 Freely falling objects

Galileo and an exceedingly impressive demo.

A couple of modifications to the kinematic equations

• Since displacement is vertical replace x with y

• a = g = –9.81 m/s2

Example: A stone is dropped from a tall building (this is against the law and very unsafe by the way). What is the vertical displacement of the stone after 4.00 s? What is its velocity at this point?

Example: A melon is thrown upward from the top of a tall building with an initial velocity of 20.0 m/s. Find the a) time for the melon to reach its maximum height b) the maximum height c) the time for the melon to return to the thrower d) the velocity and displacement at t = 5.00 s.

Some notes on freely falling bodies.

• Object is not necessarily moving down, but g is downward

• Compare v and g for an object tossed upward

• An object launched upward and downward with same vo

p. 53: 37-38, 41, 43-44; 02B1.c-d

38. a) ? b) -5.8 m

44. 6.12 s

02B1

c. 240 m (a = 30 m/s2 while engine fires)

d. 8.0 s

2.7 Graphical Analysis of Velocity and Acceleration

Position vs. time graphs

The slope of a position vs. time graph is velocity.

Describe the velocity for each part of the graph.

Velocity vs. time graphs (slightly, although not intensely,

more confusing)

The slope of a velocity vs. time graph is acceleration.

Hmmm, another interesting property of velocity vs. time graphs . . .

The area under the curve for a velocity vs. time graph is

displacement.

Some for fun

3.2 Kinematics Equations in Two Dimensions

The Slow, Painful Death of the AP Physics Student

The spacecraft and the boat crossing the river

This is important – the two velocity vectors in each case are independent of each other.

Example: A spacecraft has an initial vertical velocity of 14 m/s, and a vertical acceleration of 12 m/s2. Its initial horizontal velocity is 22 m/s and its horizontal acceleration is 24 m/s2. a) Find the final horizontal velocity and horizontal displacement when t = 7.0 s. b) Find the final vertical velocity and vertical displacement. c) Find the final velocity.

3.3 Projectile Motion

An object launched horizontally (an instructive and illustrative figure)

An object launched at an angle above the horizontal (note the expression for the components)

Example: A diver dives horizontally from a cliff. The diver’s vertical displacement is 50.0 m and the horizontal displacement is 90.0 m. What is the horizontal velocity?

Example: A football is kicked with an initial velocity of 20.0 m/s at an angle of 37.0º above the horizontal. Find a) the maximum height b) the time the ball is in flight and c) the horizontal displacement.

Another punt: A football is kicked from an initial height of 1.0 m with an initial velocity of 20.0 m/s and an angle of 37.0º above the horizontal. Find the a) time the ball is in flight b) the horizontal displacement and c) the final velocity.