1. Motion in One Dimensiondx dt x t
Physics 2053
Lecture Notes
Motion in One Dimension (2053)

2. In the study of kinematics, we consider a moving object as a particle.
Motion in 1 Dimension v 
In the study of kinematics, we consider a moving
object as a particle.
A particle is a point-like mass having infinitesimal
size and a finite mass.
Motion in One Dimension (2053)

3. = 6 m - 2 m Motion in 1 Dimension Displacement
The displacement of a particle is defined
as its change in position. x
Dx = x - xo
= 6 m - 2 m
= 4 m
(m) -6 -4 -2 2 4 6
Note: Motion to the right is positive
Motion in One Dimension (2053)

4. = -6 m - 6 m Motion in 1 Dimension Displacement
The displacement of a particle is defined
as its change in position. x
Dx = x - xo
= -6 m - 6 m
= -12 m
(m) -6 -4 -2 2 4 6
Note: Motion to the left is negative
Motion in One Dimension (2053)

5. = (2 m) - (-6 m) Motion in 1 Dimension Displacement
The displacement of a particle is defined
as its change in position. x
Dx = x - xo
= (2 m) - (-6 m)
= 8 m
(m) -6 -4 -2 2 4 6
Note: Motion to the right is positive
Motion in One Dimension (2053)

6. Velocity is represented displacement-time graph
Motion in 1 Dimension
Average velocity
The average velocity of a particle is defined as x x1 x2 t1 t2 Dx Dt
Velocity is represented
by the slope on a
displacement-time graph t
Motion in One Dimension (2053)

7. The average speed of a particle is defined as
Motion in 1 Dimension
Average speed
The average speed of a particle is defined as
Motion in One Dimension (2053)

8. Acceleration is represented
Motion in 1 Dimension
Average acceleration
The average acceleration of a particle is defined
as the change in velocity Dvx divided by the time
interval Dt during which that change occurred. v v1 v2 t1 t2 Dv Dt
Acceleration is represented
by the slope on a
velocity-time graph t
Motion in One Dimension (2053)

9. Instantaneous acceleration
Motion in 1 Dimension
Instantaneous acceleration
The instantaneous acceleration equals the derivative
of the velocity with respect to time v t Dv Dt
Instantaneous acceleration
is represented by
the slope of a
velocity-time graph
Motion in One Dimension (2053)

10. Displacement, velocity and acceleration graphs x
Motion in 1 Dimension
Displacement, velocity
and acceleration graphs x
The slope of a displacement-time
graph represents velocity t v
The slope of a velocity-time
graph represents acceleration t a t
Motion in One Dimension (2053)

11. Displacement, velocity and acceleration graphs x
Motion in 1 Dimension
Displacement, velocity
and acceleration graphs x
The area under a velocity-time
graph represents displacement. Dx t v
The area under an acceleration-time
graph represents change in velocity. Dv t a Dt t
Motion in One Dimension (2053)

12. Definitions of velocity and acceleration
Motion in 1 Dimension
Definitions of velocity and acceleration
Average velocity
Average acceleration
Motion in One Dimension (2053)

13. ? Motion in 1 Dimension For constant acceleration
An object moving with an initial velocity vo undergoes
a constant acceleration a for a time t. Find the final velocity. vo ? a
time = 0
time = t
Solution:
Eq 1
Motion in One Dimension (2053)

14. What are we calculating?t a DV
Motion in One Dimension (2053)

15. ? Motion in 1 Dimension For constant acceleration
An object moving with a velocity vo is passing position xo when it undergoes a constant acceleration a for a time t. Find the object’s final position.
time = 0
time = t xo ? a vo
Solution:
Eq 2
Motion in One Dimension (2053)

16. What are we calculating?t vi v at
Motion in One Dimension (2053)

17. Solve Eq 1 for a and sub into Eq 2:
Motion in 1 Dimension
Eq 2
Eq 1
Solve Eq 1 for a and sub into Eq 2:
Eq 3
Solve Eq 1 for t and sub into Eq 2:
Eq 4
Motion in One Dimension (2053)

18. Motion in 1 Dimension
More Graphs
Motion in One Dimension (2053)

19. -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 6
Motion in One Dimension (2053)

20. -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 6
Motion in One Dimension (2053)

21. -6 -5 -4 -3 -2 -1 1 1 2 3 4 5 6
Motion in One Dimension (2053)

22. 6 5 4 3 2 1 1 2 4 6 8 10 12 -1 -2 -3 -4 -5 -6
Motion in One Dimension (2053)

23. 6 5 4 3 2 1 1 2 4 6 8 10 12 -1 -2 -3 -4 -5 -6
Motion in One Dimension (2053)

24. 6 5 4 3 2 1 1 2 4 6 8 10 12 -1 -2 -3 -4 -5 -6
Motion in One Dimension (2053)

25. m 6 5 4 3 2 1 1 2 4 6 8 10 12 -1 s -2 -3 -4 -5 -6
Motion in One Dimension (2053)

26. 6 m 4 2 2 4 6 8 10 12 -2 s -4 -6 2 v 1 t 4 8 12
(s) -1
(m/s) -2 -3
Motion in One Dimension (2053)

27. 6 m 4 2 2 4 6 8 10 12 -2 s -4 -6 2 v
+8 m 1
+4 m t 4 8 12
(s) -1
(m/s)
-12 m -2 -3
Motion in One Dimension (2053)

28. 4 8 12 16 20 24 28
(s) x 4 8 12 16 20 24 28
(m) 1 2 3 t 5
Motion in One Dimension (2053)

29. (s) x 4 8 12 16 20 24 28
(m) 1 2 3 t 5 1 2 3 4 5 t
(s) 6 8 10 v
(m/s)
Displacement
25 m
Motion in One Dimension (2053)

30. Review: Definitions Average velocity Average acceleration
Kinematics with Constant Acceleration
Motion in One Dimension (2053)

31. Review: t x v a t x v a Dt Dv Dx
Motion in One Dimension (2053)

32. Problem Solving Skills
1. Read the problem carefully
2. Sketch the problem
3. Visualize the physical situation
4. Strategize
5. Identify appropriate equations
6. Solve the equations
7. Check your answers
Motion in One Dimension (2053)

33. END