Unit 1 Flashcards
Scalar and vector quantities
- Magnitude (number/quantity)
- Direction (up, down, left, right, north…)
Position, distance and displacement
Position - vector quantity relative to a reference point
Displacement - change in position (vector quantity)\
Distance - scalar quantity based on path travelled
Distance ≥ displacement
Algebra
- One direction is taken to be positive (right, up, forward, etc.) while the other is negative (left, down, backwards, etc.)
- The numbers are added together to find the net or resultant vector quantity
- The sign of the final quantity indicates the direction
Scale Drawings
- Using a number line as a reference (0 position), the vectors are alined “tip to tail”
- The difference between the start point and the end point give both the magnitude and direction of the net or resultant vector quantity
Scalar quantity
Speed (v)
Vector quantity
Velocity
Units
m/s = ms-1 km/h = kmh-1
Formula
Distance / time = speed
d / t = v
Types of Speed (or Velocity)
Constant - Speed does not change Instantaneous - At and instant in time, speed travelling Average - Total distance / total time
What is Acceleration
It is a change in speed:
- Speeding up (+)
- Slowing down (-)
- Changing directions
Velocity vs. Acceleration
Velocity - rate at which displacement changes
- Velocity = change in displacement / change in time
Acceleration - rate at which velocity changes
- Acceleration = change in velocity / change in time
- Acceleration = (final velocity - initial velocity) / change in time
Force
- Can cause a change in velocity
- Can cause a change in direction
Average Acceleration
Vector quantity
- Needs units and direction
- m/s2 = ms-2
- km/h / 3.6 = m/s and m/s • 3.6 = km/h
Positive and negative acceleration
- Speeding up (+)
- Slowing down (-)Formulas
- vf = vi + at (no d)
- d = vit + ½ at2 (no vf)
- d = vft + ½ at2 (no vi)
- vf2 = vi2 +2ad (no t)
- d = ½(vf+vi)t (no a)
Graphing Acceleration
Acceleration and d - t graphs
- Change in y / change in x = change in d / change in t = slope or velocity
Acceleration and v - t graphs
- Change in y / change in x = change in v / change in t = slope or acceleration
v - t - d Formula
d / t = v
Constant value near the surface of the earth
Gravity
- Has to be close to the gound
- The further you get, the weaker gravity is
- Acceleration = gravity = -9.8 m/s2
Effect of air resistance
- Reduce the net (total) acceleration
- The lighter the item, the slower the acceleration
- Air resistance is the only things that affects the speed of falling, only affected by shape and size, not mass*
Terminal velocity
- Maximum speed
- Constant
- Frequency and force of collision is in proportion (∝) to speed
Vector Addition: Scale Drawings
Step 1: Establish your scale
Step 2: Draw the first vector, beginning at the origin (displacement or velocity). You will need to use a ruler and protractor to ensure your vector is the right length and the right direction. Ex: 20m[30º W of N]
Step 3: Draw the second vectorm again taking into account length and direction, beginning at the end of the first vector. Repeat for as many vectors as are included in the question
Step 4: Draw in the resultant (net) vector, from the start of the first vector to the end of the last vector. Measure the length (ruler) and direction (protractor) of the resultant vector. Use your scale to convert the length back into the appropriate units
Adding Vectors: Algebra
Step 1: Resolve vector into x and y components
- Through the angle : COS
- Away from the angle: SIN
Step 2: Add x (horizontal) components. Add y (vertical) components. ** Pay attention to the sign (+ or -) of each vector
Step 3: Recombine x and y using the pythagorean theorem. This gives you the magnitude of the resultant vector
Step 4: Use trigonometry to determine the starting angle of the resultant vector. This gives you the direction of the resultant vector
