Kinematics Formulae & Problems Day #1

Recall From a position-time graph: From a velocity-time graph: The slope yields velocity From a velocity-time graph: The slope yields acceleration The area under the curve yields displacement We will use these facts to derive the kinematics formulae.

Using a d-t graph… Using the slope formula: (t2, ) (t1, ) ** Only formula for uniform motion.

Using a v-t graph… Using the slope formula: (t2, ) (t1, ) t

Using a v-t graph #1 Calculating the area of a triangle and rectangle: Aside:

Using a v-t graph #2 Calculating the area of rectangle and subtracting a triangle: (t2, ) (t1, ) t

Using a v-t graph #3 Calculating the area of a trapezoid: (t2, ) b h a

The Final Kinematics Formula…

Example #1 A car drives at a constant speed of 108km/h What is it’s speed in m/s How far does it travel in 60s (answer in m) How long would it take to drive 3.0km?

Example #2 If the car in 1) has to stop suddenly, find The acceleration of the car if it stops in 6 seconds The car’s stopping distance The car’s stopping distance if the car was moving 10% faster What does this tell you about speeding?