Mechanics - Kinematics •Define : • Displacement – distance & direction from reference point Dx , Dy, Dz. • Pos or neg sign gives direction. • Velocity – rate & direction object changes in position Dx /t or s/t. • sign follows displacement. • Acceleration – rate change of velocity Dv /t. • Sign give change in vel – not direction.
Mechanics - Kinematics. Define : Displacement – distance & direction from reference point D x , D y , D z . Pos or neg sign gives direction. V elocity – rate & direction object changes in position D x /t or s/t. sign follows displacement. - PowerPoint PPT Presentation
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Mechanics - Kinematics• Define:
• Displacement – distance & direction from reference point Dx , Dy, Dz.
• Pos or neg sign gives direction.
• Velocity – rate & direction object changes in position Dx /t or s/t.
• sign follows displacement.
• Acceleration – rate change of velocity Dv /t.• Sign give change in vel – not direction.
Velocity• Average velocity = s tot/ t tot.
• Instantaneous vel is a limit. • Can find from slope of tangent to point.
Ex 1: A bus travels north 180 km in 2.2 hours. It stops for 30 minutes turns and drives 60 km south in 45 min. What is its average velocity in km/h.
• vav = stot / t tot.
• 34.8 km/h.
Kinematics Equations
• IB Tables pg 6
• Uniform/constant acceleration: Dv same increment.•
• u = vi
• v = vf
• s = displ.
• a = Dv/t
Acceleration of gravity g remarks.
• Constant/uniform -9.81 m/s2 on Earth.• Negative sign is arbitrary!• Often use 10 m/s2 as estimate.• Air resistance in atmosphere causes objects to
reach terminal fall velocity after falling for a time.
• Wind/Air resistance increases with speed. Fuel efficiency in cars better at slower speeds.
Relative MotionEx 2:• You are standing on a railway platform. A is train
moving at 25 m/s to the right. On it is a passenger walking to the right at 2 m/s. What is his velocity relative to you?
• 27 m/s.
• If the velocity of object A, relative to a fixed point is VA, the velocity of object B, relative to the same fixed point is VB, then the velocity of A relative to B is the vector difference: is VA - VB.
Ex 3:
Car A is traveling 15 m/s and is overtaken by car B which is moving in the same direction at 18 m/s. What is the velocity of car B relative to car A?• Vb – Va = • 3 m/s.
• What is the velocity of Car A relative to Car B?• Va – Vb - 3 m/s
Ex 4: A boat heads north across a river 90 m wide. The speed of the boat relative to the shore is 1.8 m/s but the river pushes the boat east at 1.2 m/s.
A) What is the speed of the boat relative to the water?
B) How far will it land downstream when it arrives at the opposite shore?
• 2.2 m/s• 60-m.
Practice Sheet “IB Kinematics Questions”
IB Motion Graph Review
Distance/Position/Displacement Time GraphsConstant vel.
Starting point
Slope = Velocity
Slower Velocity
Positive Negative Quadrants
Where object is w/ref to starting point.
10
30
• What is the object’s:• a. displacement• distance
Constant Velocity/Speed
Constant / Uniform Acceleration. On velocity time graph accl. is slope of straight line.
+ or neg a shown?
What’s going on here physically?
Sign of velocity is direction of motion shown by the quadrant.
What does this show?
What does -v mean?
What does the sign of slope mean?
Displacement = Area Under Curvev = d/t then, vt = d.
To find displacement, calc area of triangle + rectangle.
When is object back at start point?
+ area must = - area
Acceleration – time graphsGraph d-t, v-t, a-t tossed ball & caught at same height.
In Class. Kerr pg 39 Ex 2.1 #1Hwk Kerr pg 71 Topic 2.1 #1-4.