1. Introduction to Motion
Motion in One Dimension

2. Basic Vocabulary For starters…
Scalar quantity: A quantity with only a magnitude. (weight, time)
Vector quantity: A quantity with a magnitude and direction
The direction can be a + or a –
45 m/s. 75 mph east. -4 m/s2

3. Basic Vocabulary/Concepts
Distance vs. Displacement
distance is how far something has traveled, displacement is the distance from starting point to ending point.
Speed vs. Velocity
Speed is a scalar quantity, velocity is a vector quantity
Reference frame: from where is this system being observed?
“is the object moving toward you or away?”
Rate: How something change over time
Velocity: the rate of change in distance
Acceleration: the rate of change in velocity

4. df = di + vit + at2 2 The Distance Formula
This is the full distance formula. Most of the time you won’t need the entire thing. (If there is no acceleration, that whole part equals zero.)

5. Setting a Reference Frame
Generally, the positive direction is toward the right.
0.55 m/s
Reference Frame
m/s
Reference Frame

6. For objects moving vertically, positive is generally away from the surface (and you).
375 m/s
- 375 m/s
Reference Frame
There may be times when you want to have a different reference frame, but make sure your math is ALWAYS consistent with your reference frame!

7. Steps to Solving Physics Problems
Draw a picture with a reference frame.
Label quantities you know. Make sure you’re using consistent units.
Write out needed formulas and solve algebraically for the unknown variable. Figure out what you need to do.
Plug in the values you know into the formula and solve. Sometimes you need to solve one formula to get a value for a second formula.

8. Solving Motion Problems in One Dimension
A snail is moving at 0.01 m/s across a road. How long will it take before it travels 20 meters?

9. Solving Motion Problems in One Dimension
A second snail starts on the other side of the road and moves toward the first snail at 0.02 m/s. Where on the road is that snail after 45 seconds?

10. Solving Motion Problems in One Dimension
A snail starts crossing a 20 meter road at 0.01 m/s. At the same time, a second snail begins to cross the same road in the opposite direction at 0.03 m/s. Where do they meet on the road and how long does it take?

11. Solving Motion Problems in One Dimension
A car that is already 1.5 km down the road is moving at a constant velocity of 15 m/s. Another car turns onto the same road and travels at twice the velocity as the first car. How far down the road do they meet and how long does it take?

12. Acceleration Acceleration: the rate of change in velocity
Speeding up = positive acceleration
Slowing down = negative acceleration

13. Turning Acceleration
Velocity is a vector, meaning it has both magnitude and direction. Therefore, if the direction changes, the velocity has changed.
So, turning is a type of acceleration, even if you remain at a constant speed!

14. v2 a = r v = radial velocity r = turning radius
Turning acceleration = centripetal acceleration v2
a = r
v = radial velocity
r = turning radius

15. Other acceleration formulas
vf = vi + at
vf2 = vi2 + 2aΔd
Which equation you’ll use depends on which variables you’re given.

16. Solving Motion Problems in One Dimension
A car goes from 0 to 40 m/s in 2.5 seconds. What is the car’s acceleration?
A car is traveling 50 m/s when the driver slams on the breaks. It comes to a stop in 1.5 seconds. What was the car’s acceleration?

17. Solving Motion Problems in One Dimension
A car starts at 20 m/s and accelerates at a rate of 4.5 m/s2 for 5 seconds. What is the car’s final speed?

18. Solving Motion Problems in One Dimension
A car starts with an initial velocity of 10 m/s and accelerates at 2.5 m/s2 for 10 seconds. How far does the car travel in that time?

19. Solving Motion Problems in One Dimension
A Dolorean starts from rest and accelerates at 10 m/s2 until it reaches a final velocity of 39.1 m/s (88 mph). How much distance has it covered in that time?