Mechanics K Warne

CAPS Requirements Average speed, average velocity, acceleration At the end of this section you should be able to... Average speed, average velocity, acceleration   · Define average speed as the distance travelled divided by the total time and know that average speed is a scalar quantity. · Define average velocity as the displacement (or change in position) divided by the time taken and know that average velocity is a vector quantity. · Calculate average speed and average velocity for one dimensional motion. · Convert between different units of speed and velocity, e.g. m×s-1, km×h-1. · Define average acceleration as the change in velocity divided by the time taken. · Differentiate between positive acceleration, negative acceleration and deceleration · Understand that acceleration provides no information about the direction of motion; it only indicates how the motion (velocity) changes. Identify and underline/highlight exactly what you need to learn! Description of · Describe in words and distinguish between motion with uniform velocity and uniformlyaccelerated motion. motion in words & diagrams

Position? ? 360o/0 N NE 45o 315o NW 90o 270o SW SE 135o 225o 180o Position of an object is always defined relative to other objects. Compass points. Absolute bearings. (From North) always taken to the right. E W S N NE 45o NW SW SE 90o 135o 180o 225o 270o 315o 360o/0

Displacement & Distance (Recap) Distance = Path traveled Home School B A Straight Line distance = displacement Displacement is a VECTOR – it has both MAGNITUDE and DIRECTION Displacement = distance traveled in a straight line

Negative Displacement 1. Moving back to start. Displacement (decreasing) = distance increasing (positive) S = 2. Moving away in reverse direction. Displacement –

Units of Distance & Displacement 1/10 (10-1) 1/100 (10-2) 1000 (103) 1/1000 (10-3) 100 (102) 10 K m Hm Dm m dm cm mm 1 m Dm Hm Km dm cm mm 1m = ……Dm = ……..Hm = ……..Km 1m = ….dm = …….cm = ………..mm

Units of Distance & Displacement Convert the following to m. 5 cm 20 mm 40 km 2 dm 10 Hm 0.1 cm 0.11 dm 0.506 Dm Length of your foot (m) Your height (Km) Lab dimensions (mm)

Speed & Velocity Path traveled * B * A s |        …. |        Average Speed = …. Uniform velocity V = = …. …. Position (distance & displacement) is changing by the _________________ every second. Average Velocity = …………. ………….. V = = …. ….

Instantaneous velocity = Speed & velocity Speed is a measure of the rate at which you are moving. (relative to something usually the ground.) Velocity is the rate at which your displacement changes. It includes the direction of movement. Instantaneous Velocity is the velocity at a particular instant. (very small time interval) Average velocity is the average of all the instantaneous velocities between two points or the total displacement divided by total time.. Distance time Speed = displacement time Velocity = (+ direction) displacement Short time (<< 1) Instantaneous velocity = V1 + V2 ... No of V’s displacement Time Average velocity = or

Mechanics Task Create either a spreadsheet or a PowerPoint slide (or a combination of both or other program) – to simulate a car speedometer, odometer and clock and use them to illustrate the concepts of instantaneous velocity and average velocities.

Average Speed & Velocity Example ● A ● B A rugby player runs around three sides of a rugby field to get from point A to point B as shown in the sketch. Calculate his average speed and average velocity if he completes the run in 30 seconds.

Negative Velocity 1. Moving back to start ∆s - S1 V = = …. ∆t + S2 Displacement …...: Velocity ……. (positive - …………..) ∆s ∆t - + S1 V = = …. S2 2. In reverse direction from starting point Displacement < 0 .: V < 0 (_______) ∆s ∆t - + V = Displacement – _________________ increasing = distance increasing (____________)

Units of Velocity Convert between different units of speed and velocity, e.g. 60 km.h-1 ?? m.s-1,

Example: An athlete runs one lap of a 400m track A-A in 60s at constant (uniform) speed. Find:- 1. distance A-B 2. displacement A-B 3. average speed A-B 4. average velocity A-B 5. Average velocity A-A A B

A B Example: An athlete runs one lap A-A in 60s at constant (uniform) speed. distance A-B = 200m displacement A-B Circum circle = 2r .: 200 = d .: d = 200/= 63.66 m S(A-B) = (63.66)2 + (100)2 =  14 052.85 m = 118.5 m towards B average speed A-B v = s/t = 200/30 = 6.67 m.s-1 average velocity A-B v = s/t = 118.5/30 = 3.95 m.s-1 towards B Average velocity A-A v = s/t = 0/60 = 0

Changing Velocity - Acceleration .. . . . . . . . . . . . . 0m/s 120Km/h 120 km/h Average = 60 km/h X = (vi + Vf)*t /2 = (0 + 120)*10/2 = 600 km 0 km/h

Changing Velocity - Acceleration .. . . . . . . . . . . . . 0m/s 2m/s 4m/s 6m/s 8m/s 0 1s 2s 3s 4s TIME t (s) 1 2 3 4 5 6 FInal Total Time INSTANTANEOUS VELOCITY Inst v (m/s) 8 10 12 AVERAGE VELOCITY in EACH SECOND av v (m/s) Average Velocity DISPLACEMENT X (m) Total displacement EQUIVALENT UNIFORM VELOCITY Unfm v The ………………….. VELOCITY at any point is …………………………… the INSTANTANEOUS VELOCITY. The AVERAGE VELOCITY over an ……………………… is ……………….. to the INSTANTANEOUS VELOCITY at the ……………………… of the interval.

Changing Velocity - Acceleration 14 12 10 8 6 4 2 ………………Velocity ………… Velocity TIME t (s) 1 2 3 4 5 6 Total Time INSTANTANEOUS VELOCITY Inst v (m/s) 8 10 12   AVERAGE VELOCITY /s av v (m/s) Average Velocity DISPLACEMENT s (m) 9 16 25 36 Total displacement EQUIVALENT UNIFORM VELOCITY Unfm v

Changing Velocity - Acceleration 14 12 10 8 6 4 2 Instantaneous Velocity – actual velocity an any instant Average Velocity - The AVERAGE VELOCITY at any point is HALF the INSTANTANEOUS VELOCITY. The AVERAGE VELOCITY over an interval is EQUAL to the INSTANTANEOUS VELOCITY at the midpoint of the interval .

Acceleration |       V1 = 1m.s-1 |       V1 = 1m.s-1 Velocity ……………… – you travel ……………… every second. Acceleration is the ……… of ……………. of velocity. In SI units, acceleration is measured in ………………….(………). V2 = 4m.s-1 2s a = Positive acceleration A > 0 Velocity increasing

Deceleration |       0m.s-1 |       0m.s-1 Velocity ………………. – you travel ……………….. distance every second. Acceleration is the rate of change of velocity. 2s a = 4m.s-1 ……………. acceleration a 0 Velocity …………….

Instantaneous Velocity (m.s-1) Uniform acceleration For. Acceleration = rate of change of velocity V t a = An object that falls from rest. Time (s) Displacement (m) Average Velocity Instantaneous Velocity (m.s-1) Acceleration (m.s-2) 5 20 45 4 80 125 6 180 1 2 3

CAPS Requirements  Average speed, average velocity, acceleration (At the end of this section you should be able to...) I can now...  Average speed, average velocity, acceleration   · Define average speed as the distance travelled divided by the total time and know that average speed is a scalar quantity. · Define average velocity as the displacement (or change in position) divided by the time taken and know that average velocity is a vector quantity. · Calculate average speed and average velocity for one dimensional motion. · Convert between different units of speed and velocity, e.g. m×s-1, km×h-1. · Define average acceleration as the change in velocity divided by the time taken. · Differentiate between positive acceleration, negative acceleration and deceleration · Understand that acceleration provides no information about the direction of motion; it only indicates how the motion (velocity) changes. Now tick off and make sure everything has been covered! Description of · Describe in words and distinguish between motion with uniform velocity and uniformlyaccelerated motion. motion in words & diagrams