1. To describe motion we first need to define a reference frame
Origin
Positive and Negative directions
N is positive; E is positive usually
Clock
Reference Frame

2. Displacement Change in an object’s position Vector quantity
Δx = x – x0
SI units: m
Other units: cm, ft, inches, miles Δx x x0
Displacement

3. Distance How much ground an object has covered during its motion.
Scalar quantity
Always positive
SI units: m
Other units: cm, ft, inches, miles x x0
Distance

4. Speed How fast an object is moving 𝑆𝑝𝑒𝑒𝑑= 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐸𝑙𝑎𝑝𝑠𝑒𝑑 𝑇𝑖𝑚𝑒
𝑆𝑝𝑒𝑒𝑑= 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐸𝑙𝑎𝑝𝑠𝑒𝑑 𝑇𝑖𝑚𝑒
Always positive
SI units: m/s
Other units: cm/s; miles/hr; km/hr x x0
Speed

5. Velocity Velocity is the rate at which an object changes position
𝑣= 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑡𝑖𝑚𝑒 = ∆𝑥 ∆𝑡 = 𝑥−𝑥0 𝑡−𝑡0
Vector quantity
Magnitude = speed
Direction = direction of displacement
SI units : m/s
Velocity

6. Acceleration 𝑎𝑎𝑣𝑔= ∆𝑣 ∆𝑡 = 𝑣 −𝑣0 𝑡 −𝑡0 SI units: m/s/s or m/s2
𝐴𝑣𝑔 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛= 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑡𝑖𝑚𝑒
𝑎𝑎𝑣𝑔= ∆𝑣 ∆𝑡 = 𝑣 −𝑣0 𝑡 −𝑡0
SI units: m/s/s or m/s2
Vector quantity
For an object moving at constant velocity, a=0
Acceleration

7. Kinematics Equations 𝑣=𝑣0+𝑎𝑡 𝑥=𝑥0+𝑣0𝑡+ 1 2 𝑎𝑡2 𝑥= 1 2 𝑣0+𝑣 𝑡
Special case: constant velocity where a=0
𝑣=𝑣0+𝑎𝑡
𝑥=𝑥0+𝑣0𝑡+ 1 2 𝑎𝑡2
𝑥= 𝑣0+𝑣 𝑡
𝑣2=𝑣02+2𝑎𝑥
𝑣=𝑣0=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑥=𝑥0+𝑣𝑡
∆𝑥=𝑣𝑡
Kinematics Equations

8. Example #1 Object Initial position (x0) Final Position (x) Time 1
Use the data to determine the displacement for each of the objects:
Object
Initial position (x0)
Final Position (x)
Time 1
+2.0 m
+6.0 m
0.5 s 2 3
-3.0 m
+7.0 m
Example #1
+4.0 m
-4.0 m
+10 m

9. Example #2 Object Initial position Final Position Time 1 +2.0 m +6.0 m
Use the data to determine the average velocity for each of the objects:
Object
Initial position
Final Position
Time 1
+2.0 m
+6.0 m
0.5 s 2 3
-3.0 m
+7.0 m
Example #2
+8.0 m/s
-8.0 m/s
+20 m/s

10. Andy Green in the car ThrustSSC set a world record of 341
Andy Green in the car ThrustSSC set a world record of m/s in The car was powered by two jet engines, and it was the first one officially to exceed the speed of sound. To establish such a record, the driver makes two runs through the course, one in each direction to nullify wind effects. The car first travels from left to right and covers a distance of 1609m in a time of 4.740s. In the reverse direction, the car covers the same distance in 4.695s. Determine the average velocity for each run.
Example #3
m/s
m/s

11. Two toy cars are placed 10 meters apart on a track
Two toy cars are placed 10 meters apart on a track. The red car is placed at the origin and moves to the right at a speed of 1.2 m/s. The blue car is placed at the +10m mark and moves to the left at a speed of 3.1 m/s. At what time will the two cars meet? At what position will the two cars meet?
Example #4
2.33 s
2.79 m

12. 5. (HW #13) You are driving home from school steadily at 65 mph for 130 miles. It then begins to rain and you slow to 55 mph. You arrive home after driving 3 hours and 20 minutes.
(a) How far is your hometown from school?
(b) What was your average speed?
Example #5
miles
61 mph