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.