Chapter+1.1+-+Mechanics+Review

Chapter 1.1 - Mechanics Review //By Matthew Pritchard 2009// __ Scalars and Vectors __

”// S // //comes before V,// //1 comes before 2,// //So Scalars require 1 quantity whereas Vectors require 2// ”

eg, Distance, Speed, Time, Mass, Energy
 * Scalars** – Scalars only need a Magnitude (amount)

eg, Displacement, Velocity, Acceleration, Force, Momentum
 * Vectors** – Vectors need a Magnitude (amount) __aswell__ as a Direction (left/right, forward/back)

X - Distance (m) || //Add Direction// || X - Displacement (m right →) || S - Speed (m/s ˉ¹) || //Add Direction// || V - Velocity (m/s ˉ¹ upwards ↑) || A - Acceleration (m/s ˉ² left ←) ||
 * Scalar (1 Quantity)** ||
 * Relationship** ||
 * Vector (2 quantities)** ||
 * Vector (2 quantities)** ||

__ Vector Techniques __ When a vector is multiplied by a scalar (eg, a number) the magnitude changes to that factor. x = 2m up 2x = 4m up 8x = 16m up
 * Multiplying Vectors**

1+2=3. Simple
 * Adding Scalars**

When Vectors are added direction must be taken into account:
 * Adding Vectors**

6m North

+ 8m East

= 10m NorthEast

__A____ verages __

Time Taken ∆t **Average Velocity** = __Displacement__ = __x__ Time Taken ∆t **Average Acceleration** = __Change in Velocity__ = __∆v__ Change in Time ∆t *Note: ∆v (Change in Velocity) is equal to v – u (Final Velocity – Initial Velocity) __ Conversions __ Minutes → Seconds ___m x 60 =__ _s Seconds → Minutes ___s ÷ 60 =__ _m Metres Per Second → Kilometres Per Hour ___m/s x 3.6 =__ _k/h Kilometres Per Hour → Metres Per Second ___k/h ÷ 3.6 =__ _m/s __ Matt’s Awesome Special Questions __
 * Average Speed** = __Distance Travelled__ = __d__
 * Exercise 1.1**

I leave for school and head East for 5km, I then realise im going the wrong way and turn around and travel West for 12km to get to school.

1.) What is my Distance Travelled?

2.) What is my Displacement?

If my total time is 15 minutes calculate:

3.) My Average Speed?

4.) My Average Velocity?

I get to school to find out that it is a student free day, tired but happy I walk all the way home. This takes an extra 5 minutes.

5.) What is my new total distance travelled?

6.) What is my new displacement when I arrive home?

7.) What is my Average Speed?

8.) What is my new velocity when I arrive home? Explain how, when I have walked so far that it is my velocity.

__ Trigonometric Uses in Physics __





__ Graphing Motion __ A ball starts from rest and moves forward at 2m/s for 3 seconds, it then stops for 5 seconds then rolls backwards at 1m/s for 8 seconds when it then returns to its starting point in 4 seconds

-Position Time Graph

A Car begins with a velocity of 4m/s North and decelerates to rest in 6 seconds where it remains for 2 seconds then continues in the same direction with a constant velocity of 5m/s

-Velocity Time Graphs

A Car from rest accelerates uniformly by 1m/s for 5 seconds, it then retains that speed for 3 seconds, it then decelerates at 5m/s for the next 7 seconds.

-Acceleration Time Graph

__ Motion Equations __ v=u+at x=½(u+v)t x=ut+½at ² x=vt-½at² v²=u²+2ax || x – Distance/Displacment (metres – m) u – Initial Velocity (metres per second – m/s ˉ¹) v – Final Velocity (metres per second – m/s ˉ¹) a – Acceleration (metres per second squared – m/s ˉ²) t – Time (seconds – s) ||