7.1 Displacement, Speed, Velocity

~35 mins taken

centre of mass §

the course does not analyse centre of mass, as it can play an effect in the function of motion.

position, distance displacement §

• position §

• position describes the location of an object in time with respect to the origin.
• position is a vector quantity, therefore it requires a direction.

• distance travelled §

• distance describes how far an object travels during a journey.
• if sophie completes three lengths of a 50m pool, the distance would be 50 + 50 + 50 = 150m
• distance is not affected by the direction, and is a variable that always increases as the object moves.
  • therefore it is a scalar quantity

• displacement §

• change in position of an object.
• takes into account only where the motion starts and finishes, so the journey in between isnt taken into account when calculating displacement.

  vector quantity displacement s = final position - initial position

• if somebody runs 100m and 100m back, displacement would still be 0 m, because the distance from the origin hasn’t changed.
• you can also calculate total displacement by summing up the individual displacements
• e.g. a car is displaced 50m right from the origin, and then displaced -50m right
• s = 50 + (-50) = 0m

speed and velocity §

• gives indication of how fast the position of an objection is changing
• speed is magnitude, velocity is a vector.

• formula §

• average or mean speed $v_{avg}=\frac{d}{t}$
• average or mean velocity $v_{avg}=\frac{s}{t}=\frac{v+u}{2}$

converting between $km{h}^{-1}$ and $m{s}^{-1}$ §

• get units, convert units
• eg km/h to m/s
• km = 1000m, h = 3600
• therefore 1000/3600
• $xkmh\times \frac{1000}{3600}=xms$
• and to convert it other way around multiply by 3.6

REVIEW §

1. a student jogs one lap of a 400 m track in 2mins, calculate:
   • her average speed: 400/120 = 3.333 m/s
   • her average velocity: s/t = 0/120 = 0 m/s
2. a girl swims ten lengths of a 25 m pool. which one or more of the following statements correctly describes her distance travelled and displacement?
   1. her distance travelled was 0.
   2. her displacement is 0
   3. her distance travelled is 250m
   4. her displacement is 250m
   5. 2 and 3 is correct
3. ant
   • +40cm
   • -10cm
   • +20cm
   • d=80cm, s=+20cm
4. cyclist
   1. 80km
   2. 20km north in the pos direction
5. lift
   1. 10m down in the negative direction
   2. 50m upwards in the pos direction
   3. 60m
   4. 50m upwards in the pos direction
6. car
   1. 400m/12s = 33.3 m/s
   2. 12.75 x 33.33 = 425m
7. cyclist 2
   1. 25/1.5 = 16.7 km/h
   2. 16.666 x 1000/3600 = 4.63 m/s
8. liam and his toy truck
   1. 9/10 = 0.9m/s
   2. 1m east / 10 = 0.1m/s east
9. mihi and her bicycle
   1. 2.5km/0.25 = 10km/h
   2. 2500/900 = 2.5/0.25 x 1000/3600 = 2.78m/s
10. athlete training
    1. 15 + 3 = 18km total
    2. s = 15km
    3. speed = 18km / 1.5h = 12km/h
    4. vavg = 15km / 1.5 = 10km/h