Mechanics: Kinematics Test Review

Unit Conversion Converting from one unit to another requires the use of conversion factors. Some common Conversion Factors: 2.54 cm = 1in100 cm = 1m 3600 s = 1 hr1000 mm = 1 m 5280 ft = 1 mi1000 m = 1 km

Example Use a t-chart to complete the conversion: Convert 25mph into m/s.

Practice Complete the following conversion on your own: Convert 75mph into m/s.

Vectors Def: A number that has a magnitude and direction. VectorsNot Vectors (Scalars)

Vectors Def: A number that has a magnitude and direction. VectorsNot Vectors (Scalars) VelocitySpeed DisplacementDistance AccelerationTime

Adding Vectors Vectors can be added together using what we know about triangles: Example: A hiker walks 10km North, then 5km East. What is his final displacement? Note: When expressing your answer, be sure to use correct Directional Notation! (All angles need to be measured from the East-West Axis)

Distance & Speed Distance and Speed are both scalars. Distance/time = Speed. Displacement and Velocity are both Vectors. Displacement/time = Velocity

Example If the hiker from the previous example completed their trip in 2hrs, what is their average speed and average velocity?

Motion: Interpreting Graphs There are two major types of motion we have looked at: 1) Objects with a constant velocity. (Left Side) 2) Objects with a constant acceleration. (Right Side)

Constant Velocity With each type of motion, there are 3 separate graphs: position vs. time, velocity vs. time, and acceleration vs. time. Position vs. Time Finding the slope of this graph will tell you the object’s velocity. Position (m) Time (s)

Constant Velocity Velocity vs. Time The slope of this graph will be acceleration of the object. Velocity (m/s) Time (s)

Constant Velocity Velocity vs. Time The area under this graph will be displacement of the object. (how far it has travelled) Velocity (m/s) Time (s) Area = b*h

Constant Velocity Acceleration vs. Time The acceleration of an object with constant velocity will always be “0”. Acceleration (m/s 2 ) Time (s)

Constant Acceleration Position vs. Time The position vs. time graph of an object with constant acceleration will always be a curve. Position (m) Time (s)

Constant Acceleration Velocity vs. Time The slope of this graph will be acceleration of the object. Velocity (m/s) Time (s)

Constant Velocity Velocity vs. Time The area under this graph will be displacement of the object. (how far it has travelled) Velocity (m/s) Time (s) Area = ½ b*h

Constant Acceleration Acceleration vs. Time The area under this graph will be the velocity of the object. Acceleration (m/s 2 ) Time (s) Area = b*h

Example Given the following graph, determine if the object is at constant velocity or constant acceleration. Using the graph, determine the object’s acceleration, and distance traveled for the whole trip. (10m/s2, 20m)

Example For the following graph, does the object have a constant velocity or constant acceleration? What is the object’s velocity? (8 m/s)

Kinematics Equations VariablesNameUnits Δxdisplacement(m) v i initial velocity(m/s) v f final velocity(m/s) aacceleration(m/s 2 ) ttime(s)

Average Velocity Example: During a race on level ground, Andra runs with an average velocity of 6.02 m/s to the East. What is Andra’s displacement after 137s? (824m)

Average Acceleration Example: A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop? (5s)

Displacement with Acceleration Example: A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5s later. Find the distance that the car travels during braking.(115.5m)

STOP here for today! Continue working on your classwork packet from Monday- individually! Use your phone as a calculator

Velocity and Displacement with Constant Acceleration A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s 2 for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off?

Final Velocity After any Displacement A person pushing a stroller starts from rest, uniformly accelerating at a rate of m/s 2. What is the velocity of the stroller after it has traveled 4.75m?

Falling Objects Often 2 Step Problems 1.) Find v f 2.) Answer problem Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. If the volleyball starts from 2.0m above the floor, how long will it be in the air before it strikes the floor?

2-D Kinematics Objects launched off cliffs: Example: The Royal Gorge Bridge in Colorado rises 321 m above the Arkansas River. Suppose you kick a rock horizontally off the bridge. The magnitude of the rock’s horizontal displacement is 45.0m. Find the speed at which the rock was kicked.