Kinematics

any object that moves through the 3-dimensional space of our universe seems to obey a few simple and fundamental rules we used graphs in the previous section of this unit to try to develop an understanding of these rules we were able to create a series of algebraic expressions which describe these rules in the form of mathematics all of these expressions had their roots based in one of the three kinds of graphs that we created in this section of the course we will be learning how to use these expressions/equations to make accurate and precise predictions about the outcomes of different scenarios

Equations For Calculating Average/Unchanging VELOCITY:    

Equation For Calculating Changing Velocities/Acceleration:  

 

How to Solve Word Problems solving word problems becomes a simple task if you attempt to solve them in a series of small steps: an acronym can be used to memorize the steps involved in solving word problems: GUES

G: Write out all Givens be sure to include 3 vital pieces of information with each given: quantity (number) unit direction (if given)

U: Identify the Unknown make sure you know what it is you’re looking for E: Write out the Equation that you must use to solve the problem solve the algebraic form of the equation for the variable that you’re looking for before you plug in givens

S: Solve the problem make sure the units attached to all quantities you’re working with don’t conflict if they do, perform the required conversions be sure to include units with your answer (and direction if working with vectors)

A boat travels a distance of 350 m in 20 seconds. Determine: Examples: A boat travels a distance of 350 m in 20 seconds. Determine: the speed of the boat (in ms-1) the speed of the boat (in kmh-1)

a.        

b. Convert to kmh-1      

Suppose a car travels at a constant speed of 10 ms-1 Suppose a car travels at a constant speed of 10 ms-1. How many metres would it move in: a) 1 s b) 1 min c) 1 h

a.        

b. Careful! Notice velocity is measured in ms-1. So, we must also put t (time) in seconds, not minutes. 1 min = 60 seconds        

c. Careful! Notice velocity is measured in ms-1. So, we must also put t (time) in seconds, not hours. 1 hour = 60 min x 60 sec = 3600 sec        

A bacterium can move at a uniform rate of 100 μms-1 A bacterium can move at a uniform rate of 100 μms-1. How long would it take this bacterium to move 1.0 m? μms-1 means micrometers per second 1 μms-1 = 0.000001ms-1 So 100 μms-1 = 0.0001ms-1 Which can also be written as 1x10-4μms-1

      Δt = 10 000s

Jules Verne wrote a book called Around the World in Eighty Days Jules Verne wrote a book called Around the World in Eighty Days. What was his average speed in ms-1 and kmh-1 if the radius of the Earth is 6400 km?

       

Convert kmh-1 to ms-1      

You live 3. 5 km from school and are going to be late for class You live 3.5 km from school and are going to be late for class! You hop in your parents car and decide to speed to try to make it to school on time. The posted speed limit is 60 kmh-1 but instead you travel 70 kmh-1 from your home to the school. How much time did you save by speeding vs obeying the speed limit?

1 – Calculate for Speed Limit        

2 – Calculate for Speeding         You save 0.008h

If it takes 0.08 s for an air bag to stop a person, what is the rate of acceleration of a person moving 13.0 kms-1 who comes to a complete stop in this time?

       

An object accelerates at 9. 8 ms-2 when falling An object accelerates at 9.8 ms-2 when falling. How many seconds does it take an object to change its speed from 4.5 ms-1 to 19.4 ms-1?

       

What is an object’s final velocity if it accelerates at 2 What is an object’s final velocity if it accelerates at 2.0 ms-2 [F] for 2.3 s from a velocity of 50 kmh-1 [F]? (F = forward)

Careful! Must convert! 13.9ms-1 = 50kmh-1   Careful! Must convert! 13.9ms-1 = 50kmh-1 This is the formula for acceleration, just algebraically manipulated