Kinematics in One Dimension

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

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 2

A Special Case: Constant Acceleration Using the definitions we can derive Caution: These assume accelerationis constant. From the above you can get: Physics 1D03 - Lecture 2

Example: Free Fall. (“Free fall” means the only force is gravity; the motion can be in any direction). • 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”. Physics 1D03 - Lecture 2

Quix 1 A block is dropped from rest. It takes a time t1 to fall the first third of the distance. How long does it take to fall the entire distance? • t1 • 3t1 • 9t1 • None of the above Physics 1D03 - Lecture 2

Example 1 A particle’s position is given by the function: x(t)=(-t3+4t) m • what is the velocity at t=3 s ? • what is the acceleration at 3 s ? • make a sketch of the motion Physics 1D03 - Lecture 2

Example 2 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 ? Physics 1D03 - Lecture 2

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 2

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 2

Vector Review • Scalars and Vectors • Vector Components and Arithmetic Physics 1D03 - Lecture 2

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 2

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 2

Coordinate Systems In 2-D : describe a location in a plane y • 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 y  x 0 x Physics 1D03 - Lecture 2

By Ay Ax Bx By Cy Bx Ay Ax Cx Addition: IfA + B = C , then: Tail to Head Three scalar equations from one vector equation! Physics 1D03 - Lecture 2

Kinematics in One Dimension