Physics 1D03 - Lecture 21 Kinematics in One Dimension Displacement, velocity, acceleration, free fall Examples Knight: Chapters 1, 2

Physics 1D03 - Lecture 22 1-D motion can be described by scalars (real numbers with units) as functions of time: Position x(t) (displacement from the origin) Velocity v(t)=dx/dt (rate of change of position) Acceleration a(t)=dv/dt (rate of change of velocity)

Physics 1D03 - Lecture 23 Caution: These assume acceleration is constant. Using the definitions we can derive A Special Case: Constant Acceleration From the above you can get:

Physics 1D03 - Lecture 24 All objects in free fall move with constant downward acceleration: This was demonstrated by Galileo around 1600 A.D. The constant “g” is called the “acceleration due to gravity”. Example: Free Fall. (“Free fall” means the only force is gravity; the motion can be in any direction).

Physics 1D03 - Lecture 25 Quix 1 A block is dropped from rest. It takes a time t 1 to fall the first third of the distance. How long does it take to fall the entire distance? a) t 1 b)3t 1 c)9t 1 d)None of the above

Physics 1D03 - Lecture 26 Example 1 A particle’s position is given by the function: x(t)=(-t 3 +4t) m a)what is the velocity at t=3 s ? b)what is the acceleration at 3 s ? c)make a sketch of the motion

Physics 1D03 - Lecture 27 An object if thrown straight up with a velocity of 5m/s. What will the velocity be when it comes back to its original position ? Example 2

Physics 1D03 - Lecture 28 Example 3 A skier is moving at 40m/s at the top of a hill. His velocity changes to 10m/s after covering a distance of 600m. What is his acceleration ?

Physics 1D03 - Lecture 29 Example 3b The skier’s girlfriend is also traveling at 40m/s, but, unfortunately, after only 3s, hits a tree and her velocity ‘suddenly’ comes to 0m/s. How far did she get, given the same deceleration as in the previous question?

Physics 1D03 - Lecture 210 Vector Review Scalars and Vectors Vector Components and Arithmetic

Physics 1D03 - Lecture 211 Physical quantities are classified as scalars, vectors, etc. Scalar : described by a real number with units examples: mass, charge, energy... Vector : described by a scalar (its magnitude) and a direction in space examples: displacement, velocity, force... Vectors have direction, and obey different rules of arithmetic.

Physics 1D03 - Lecture 212 Notation Scalars : ordinary or italic font (m, q, t...) Vectors : - Boldface font (v, a, F...) - arrow notation - underline (v, a, F...) Pay attention to notation : “constant v” and “constant v” mean different things!

Physics 1D03 - Lecture 213 Coordinate Systems In 2-D : describe a location in a plane by polar coordinates : distance r and angle  by Cartesian coordinates : distances x, y, parallel to axes with: x=rcosθ y=rsinθ These are the x and y components of r x y  r ( x, y ) 0 x y

Physics 1D03 - Lecture 214 Addition: AxAx AyAy ByBy BxBx ByBy BxBx AyAy AxAx CxCx CyCy If A + B = C, then: Three scalar equations from one vector equation! Tail to Head