Physics In Motion 1-D Kinematics

Aristotle’s Notion of Motion  All objects will remain at rest unless an external force is acted upon them. If an external force is removed then an objects will come to rest on its own.  Heavier objects fall faster than lighter objects.  The Earth does not move and all other planets orbit the Earth.

 Aristotle’s concept of motion went unchallenged for nearly 2000 years, until Galileo Galilei ( ) used inclined planes to test his idea that objects not only need a force to start them moving, but a force to stop them from moving.

 Galileo also used inclined planes to test the speed of objects in free fall.

Galileo’s Notion of Motion  All objects need an external force to start moving AND an external force to stop moving.  All objects fall with the same acceleration in the absence of air resistance.  All planets in our solar system revolve around the sun.

Newton’s First Law

 Inertia is the tendency of an object to resist change in motion.  An object at rest tends to stay at rest and an object in motion tends to stay in motion, unless an external force acts upon it.  The greater the mass of an object, the more inertia it has.

Position, Distance, and Displacement  Distance is the total length of travel, but displacement is the length of travel from a starting point.  For example if you run around a 400 m track the total distance you traveled is 400 m, but your total displacement is 0 m.

Scalars vs. Vectors  A vector is a quantity that has both a magnitude (number or value) and a direction.  Examples: velocity and acceleration  A scalar only has a magnitude.  Ex: mass, density, and temperature.

Velocity  Average velocity is the change in position, divided by the time that change took.

Position vs. Time Graph  A position vs. time graph can be used to calculate the velocity of an object by calculating the slope of the graph over an interval of time.

 Acceleration is the rate of change of velocity.

Velocity vs. Time Graph  An velocity vs. time graph can be used to calculate the acceleration of an object by calculating the slope of the graph over an interval of time.

 In scenarios (b) and (c) the car is slowing down, since acceleration and velocity point in opposite directions.

Sample Problems  Your velocity changes from 60 m/s to the right to 100 m/s to the right in 20 s; what is your average acceleration?  Your velocity changes from 50 m/s to the left to 10 m/s to the right in 15 s; what is your average acceleration?

Equations for Motion at Constant Acceleration

Solving Problems for Motion at Constant Acceleration Step 1: Identify all of the variables in the problem. Step 2: List the values for your known variables. Step 3: Choose the correct equation that has all of the variables you identified in your problem. Step 4: Plug in your known variables into the equation and solve for the unknown.

Sample Problem  How much time does it take to come to rest if your initial velocity is 5.0 m/s and your acceleration is -2.0 m/s 2 ?

Sample Problem  You accelerate from 20m/s to 60m/s while traveling a distance of 200m; what was your acceleration?

Sample Problem  You have an initial velocity of 5.0 m/s. You then experience an acceleration of -1.5 m/s 2 for 4.0s; what is your final velocity?

Sample Problem  A train pulling out of Grand Central Station accelerates from rest at a constant rate. It covers 800 meters in 20 seconds. What is its rate of acceleration?

Free Falling  All objects fall towards the earth with the same acceleration.  We call this the "acceleration due to gravity" and it is represented by g.  g = 9.8 m/s 2

Free Falling An object is thrown upward with initial velocity, v o It slows down. (negative acceleration) g = -9.8 m/s 2 It stops momentarily. v = 0 g = -9.8 m/s 2 It speeds up. (negative acceleration) g = -9.8 m/s 2 It returns with its original velocity.

Sample Problem  An acorn falls from an oak tree. It takes 2.5 seconds to hit the ground. How fast was it going when it hit the ground?

Sample Problem  A ball is kicked with an initial velocity of 25m/s; how high does it go before coming to a momentary stop?

Sample Problem  An arrow is shot vertically up by a bow, and after 8 s returns to the ground level. What is the initial velocity of the arrow? How high did it go?