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1 Chapter 10 Uniformly Accelerated Rectilinear Motion

Physics 504 chapter 10 uniformly accelerated rectilinear motion

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Page 1: Physics 504 chapter 10 uniformly accelerated rectilinear motion

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Chapter 10UniformlyAcceleratedRectilinearMotion

Page 2: Physics 504 chapter 10 uniformly accelerated rectilinear motion

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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.

Page 3: Physics 504 chapter 10 uniformly accelerated rectilinear motion

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Curvilinear Motion

http://news.yahoo.com/photos/ss/441/im:/070123/ids_photos_wl/r2207709100.jpg

A particle moving along a curve other than a straight line is said to be in curvilinear motion.

Page 4: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Activity

•Page 228, Q. 1-8

•Page 196, Q. 1-3

•Lab: Walking Uniformly

•Lab: Acceleration due to Gravity

Page 5: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Final Velocity

•Velocity can be calculated if we consider it in terms of the initial velocity which has undergone acceleration or deceleration.

•v = u + at

•v = final velocity, in m/s

•u = initial velocity, in m/s

•a = acceleration, in m/s2

•t = time of acceleration, in seconds

Page 6: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Activity

•What is the final velocity of a person walking at 4 m/s who accelerates at 1 m/s2 for 5 s?

•v = u + at

• = 4m/s + 1m/s2 x 5s

• = 4m/s + 5m/s

• = 9m/s

Page 7: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Distance Covered

•Distance can be determined if the initial velocity, time and acceleration are known.

•s = ut + ½ at2

•s = distance, m

•u = initial velocity, m/s

•t = time, seconds

•a = acceleration m/s2

Page 8: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Activity

•What is the depth of a well, if when you drop a rock, it takes 5 seconds to hit the bottom?

•s = ut + ½ at2

• = 0(5) + ½ (9.81m/s2)(5s)2

= 0 + ½ (9.81)(25)•

= 122.625 m

Page 9: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Vertical Motion

•ONLY in situations where objects are moving vertically through space, is the acceleration - 9.81 m/s2.

•An object dropped has an initial velocity of 0 m/s.

•The acceleration due to gravity slows objects moving upwards and speeds up objects moving downwards.

Page 10: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Final Velocity

•The final velocity can also be calculated this way.

•v2 = u2 + 2as

•v = final velocity, m/s

•u = initial velocity, m/s

•a = acceleration m/s2

•s = distance, m

Page 11: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Short Cut

•What 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?

•v2 = u2 + 2as

• = (10 m/s)2 + 2(2m/s2)(100m)

• = 100 + 400

•v2 = 500

•v = 22.4 m/s

Page 12: Physics 504 chapter 10 uniformly accelerated rectilinear motion

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

Page 13: Physics 504 chapter 10 uniformly accelerated rectilinear motion

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

Page 14: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Activity

•Page 234, Q 1-5

•Page 238, Q 1-6

•Handout

Page 15: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Projectile Motion

•Projectile Motion

Page 16: Physics 504 chapter 10 uniformly accelerated rectilinear motion

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Sample Problem

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.

Ball tossed with 10 m/s vertical velocity from window 20 m above ground.

Page 17: Physics 504 chapter 10 uniformly accelerated rectilinear motion

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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.

x

y

0v v at 21

0 0 2x x v t at

2 20 02v v a x x

Remember:

Page 18: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Summary

•When air resistance is negligible, all freely falling objects have the same downward acceleration.

•A ball rolling down an incline has uniform acceleration.

•Acceleration due to gravity has a value of 9.81 m/s2.

•Equations derived for uniform acceleration apply to freely falling objects.

Page 19: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Summary•A

negative slope on a straight line position-time graph indicates motion in a negative direction at constant velocity.

•Average velocity = displacement/time interval

which can be taken at any 2 times on a position-time graph.

•Average speed = total distance/time interval

•Instantaneous velocity can be taken from the slope of the tangent to the curve at that time.

Page 20: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Summary

•Velocity is a vector quantity which may be found if the velocity is uniform, with velocity = displacement/time.

•Speed is a scalar quantity which may be found, if the speed is uniform, with speed = distance/time.

•The position-time graph for an object moving with uniform motion is a straight line. The slope of the straight line gives the velocity.

Page 21: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Summary

•Acceleration is the rate of change of velocity over time.

•a =Δ ע/Δt = ( 1ע- 2ע )/Δt

•On velocity-time graphs, a straight line shows that an object has a constant acceleration.

•On a velocity-time graph, the acceleration is the slope of the line.

Page 22: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Summary•A

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.

•The area under the velocity-time graph gives the displacement.

•v = u + at

•s = ut + ½ at2

•v2= u2 + 2as

Page 23: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Summary

•If the motion is in a straight line, the vector notation may be omitted and +/- signs used instead.

•A 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.

Page 24: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Summary

•The acceleration at any point on a curved velocity-time graph is the slope of the tangent to the curve at that point.

•To 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.

Page 25: Physics 504 chapter 10 uniformly accelerated rectilinear motion

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

Page 26: Physics 504 chapter 10 uniformly accelerated rectilinear motion

Activity

•Page 242, Q. 1-6