Linear Motion

1. LINEAR MOTION

2. Learning Objectives:
At the end of the chapter the students should be able to:
1. Determine distance and displacement.
2. Demonstrate the ability to calculate average velocity and instantaneous
velocity from position-time graph.
3. Calculate the average and instantaneous acceleration from a velocity-time
graph.
4. Solve problems of uniformly accelerated linear motion including free fall.

3. Distance (d) is a scalar quantity. It is the actual length the object travelled.
a. A body moving to the right b. A body initially moving 8m east and
then moved 6m north.
d= 8m + 6m = 14m
c. a body thrown up at a height h and returned to its starting point
Example 1. Find the distance of a body moving from point 1 to point 2.
Distance and Displacement
d = h + h = 2h

4. a. A body moving to the right b. A body initially moving 8m east and
then moved 6m north.
c. a body thrown up at a height h and returned to its starting point
S = 0
Displacement (S) is a vector quantity. It is a straight line that points from the object’s
initial position to its final position.
S= = 10m
direction:
θ = tan-1
= 36.90
north of east
Example 2. Find the displacement of a body moving from point 1 to point 2.
Sign convention for S:
+S -S +S -S

5. Speed (v) is scalar quantity that describes how fast the
object moves
Average speed = =
Speed and Velocity

6. Velocity (V) is a vector quantity that describes not
only how fast the object moves but as well as its
direction.
Average Velocity =
Instantaneous Velocity =
Sign convention for V:
+V -V +V -V

9. Example3. The graph shows the position of a mouse with respect to time.
a. What is its instantaneous velocity at 1s?
b. What is its instantaneous velocity at 3s?
c. What is its instantaneous velocity at 7s?
d. What is the average velocity of the mouse?
V at 1s = directed to the right
V at 3s =
V at 7s = directed to the left
V ave. = directed to the right

10. Acceleration (a) is the rate of change of velocity.
Acceleration changes the magnitude and/or direction of
velocity.
a ave =
a inst.= =
Sign convention for a:
+a -a +a -a

12. Example 4. The velocity-time graph of a man travelling from A to D is shown below.
a. What is his acceleration between AB?
b. What is his acceleration between BC?
c. What is his acceleration between CD?
a = 10m/s2
a = 0
a = -7m/s2

13. Linear motion with constant acceleration
The slope of velocity-time graph is a straight line that corresponds to acceleration.
slope = acceleration
V(m/s)
Vf
Vi
ti tf
t(s)
Equations:
at ti
=0, Vi
= Vo ,
Vf
= V
V = Vo
+ at
V2
= Vo
2
+ 2aS
S = Vo
t + ½ at2
Vave = =

15. Example 5. A car starts from rest and accelerates at 4m/s2
for 5s. It runs at
constant speed for 10s and slows down at a rate of -2m/s2
until it stops at the
intersection. What is the total distance covered?
Given:
V1
=0 V2
V2
=V3
V3
V4
=0
a 1-2
= 4m/s2
a2-3
=0 a3-4
= -2m/s2
t1-2
=5s t2-3
=10s
S1-2
S2-3
S3-4
Stotal

17. Solution:
S1-2 = ½ (4m/s2
) (5s)2
= 50m
V2 = (4m/s2
) (5s) = 20m/s
S2-3 = (20m/s) (10s) = 200m
S3-4 = = 100m
Stotal = 50m + 200m + 100m = 350m

18. Freely Falling Body
When motion of a falling body is affected by the gravitational
acceleration alone (negligible air resistance), its motion is free fall.
a = -g g= 9.80m/s2
Equations:
V = Vo
- gt
S = Vo
t - ½ gt2
V2
= Vo
2
– 2gS

20. Example 6. A ball is thrown up with a speed of 10.0m/s.
a. How far would it go up?
b. How long would it reach the maximum height?
c. What is the total time of flight?
S = = 5.10m
t = =1.02s
t = =2.04s