This document discusses uniformly accelerated rectilinear motion. It introduces kinematics, which is the study of motion without considering causes, and kinetics, which considers the forces that cause motion. Rectilinear motion refers to motion along a straight line, while curvilinear motion is along a curved path. Formulas are provided for calculating final velocity, distance, and acceleration from gravity for vertical motion. Sample problems demonstrate applying the formulas to problems involving projectile motion.

1. Chapter 10
Uniformly
Accelerated
Rectilinear
Motion
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2. Introduction
• Dynamics includes:
- Kinematics: study of the motion (displacement,
velocity, acceleration, & time) without reference to
the cause of motion (i.e. regardless of forces).
- Kinetics: study of the forces acting on a body,
and the resulting motion caused by the given
forces.
• Rectilinear motion: position, velocity, and acceleration of
a particle as it moves along a straight line.
• Curvilinear motion: position, velocity, and acceleration of
a particle as it moves along a curved line.
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3. Curvilinear Motion
A particle moving along a curve other than a straight line
is said to be in curvilinear motion.
http://news.yahoo.com/photos/ss/441/im:/070123/ids_photos_wl/r2207709100.jpg
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4. Activity
age 228, Q. 1-8
age 196, Q. 1-3
ab: Walking Uniformly
ab: Acceleration due to Gravity

5. Final Velocity
elocity can be calculated if we consider it
in terms of the initial velocity which has
undergone acceleration or deceleration.
= u + at
= final velocity, in m/s
= initial velocity, in m/s

6. Activity
hat is the final velocity of a person walking
at 4 m/s who accelerates at 1 m/s 2 for 5 s?
= u + at
= 4m/s + 1m/s2 x 5s
= 4m/s + 5m/s

7. Distance Covered
istance can be determined if the initial
velocity, time and acceleration are known.
= ut + ½ at2
= distance, m
= initial velocity, m/s

8. Activity
hat is the depth of a well, if when you drop
a rock, it takes 5 seconds to hit the
bottom?
= ut + ½ at2
= 0(5) + ½ (9.81m/s2)(5s)2
= 0 + ½ (9.81)(25)

9. Vertical Motion
NLY in situations where objects are
moving vertically through space, is the
acceleration - 9.81 m/s2.
n object dropped has an initial velocity of 0
m/s.
he acceleration due to gravity slows
objects moving upwards and speeds up
objects moving downwards.

10. Final Velocity
he final velocity can also be calculated this
way.
2
= u2 + 2as
= final velocity, m/s
= initial velocity, m/s

11. Short Cut
hat is the final velocity of a car if it starts at
10 m/s and accelerates at 2 m/s2 over a
distance of 100m?
2
= u2 + 2as
= (10 m/s)2 + 2(2m/s2)(100m)
= 100 + 400

12. Exam Question
From the top of a tower an object is thrown vertically downward with a velocity of 20 m/s.
What is the velocity of the object after it has fallen 60 metres?
A) 55 m/s
B) 50 m/s
C) 45 m/s
D) 40 m/s

13. Exam Question
A motorcyclist, travelling at a speed of 30 m/s, sees an obstacle 100 metres in front of him and
puts on the brakes. He hits it 5.0 seconds later.
If the motorcycle slows down uniformly, how fast was it going at the instant of the collision?
A) 10.0 m/s
B) 8.0 m/s
C) 6.0 m/s
D) 4.0 m/s

14. Activity
age 234, Q 1-5
age 238, Q 1-6
andout

15. Projectile Motion

16. Sample Problem
Ball tossed with 10 m/s vertical velocity from window 20 m above
ground.
Determine:
• velocity and elevation above ground at time t,
• highest elevation reached by ball and corresponding time, and
• time when ball will hit the ground and corresponding velocity.
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17. Example
A projectile is fired from the edge of a 150-m cliff with an initial
velocity of 180 m/s at an angle of 30° with the horizontal. Find
(a) the range, and (b) maximum height.
y
Remember:
v = v0 + at
x = x0 + v0t + at
1
2
2
v = v + 2a ( x − x0 )
2 2
0
x
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18. Summary
hen air resistance is negligible, all freely
falling objects have the same downward
acceleration.
ball rolling down an incline has uniform
acceleration.
cceleration due to gravity has a value of
9.81 m/s2.

19. Summary
negative slope on a straight line position-
time graph indicates motion in a negative
direction at constant velocity.
verage velocity = displacement/time interval
which can be taken at any 2 times on a
position-time graph.
verage speed = total distance/time interval

20. Summary
elocity is a vector quantity which may be
found if the velocity is uniform, with
velocity = displacement/time.
peed is a scalar quantity which may be
found, if the speed is uniform, with
speed = distance/time.
he position-time graph for an object
moving with uniform motion is a straight

21. Summary
cceleration is the rate of change of velocity
over time.
=Δ ‫/ע‬Δt = (1‫/)ע2 -ע‬Δt
n velocity-time graphs, a straight line
shows that an object has a constant
acceleration.

22. Summary
negative slope on a velocity-time graph
means that the magnitude of the velocity
is decreasing, if the object is moving in a
positive direction.
he area under the velocity-time graph
gives the displacement.
= u + at

23. Summary
f the motion is in a straight line, the vector
notation may be omitted and +/- signs
used instead.
curved velocity-time graph indicates a
changing acceleration. The average
acceleration for an interval is found by
finding the slope between two points on
the graph.

24. Summary
he acceleration at any point on a curved
velocity-time graph is the slope of the tangent to
the curve at that point.
o construct a velocity-time graph from a ticker
tape recording, mark the tape into lengths of the
same time interval. The displacement for each
interval divided by the time gives the average
velocity for that interval. Plotting the average
velocity for each interval versus the time will
yield a velocity-time graph.

25. Exam Question
A diver jumps from a height of 3.0 metres above the height of the water and touches the surface
1.0 s later.
What was his velocity when he hit the water?
A) 8.0 m/s
B) 7.0 m/s
C) 6.0 m/s
D) 5.0 m/s

26. Activity
age 242, Q. 1-6