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Intro to kinematics. The study of motion, regardless of cause. Average Speed . As far back as 300-400 BC, the ancient Greeks could calculate: Speed = distance traveled time elapsed This is a scalar with SI units of m/s. The difference between distance and displacement.
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Intro to kinematics The study of motion, regardless of cause
Average Speed • As far back as 300-400 BC, the ancient Greeks could calculate: Speed = distance traveled time elapsed This is a scalar with SI units of m/s.
The difference between distance and displacement • Symbol: We will use x for displacement • Use d for distance, however be sure to distinguish it from the d’s we use in calculus notation for differentials. • Distance is the length of the route traveled. • Displacement is how far the object traveled, i.e. “as the crow flies”, in other words, it’s a vector. • Is the odometer on your car a distance or displacement meter? • Is a quarterback concerned with the distance or displacement of the receiver when he throws a pass?
Constant speed – a special situation • Acceleration = 0 • Some objects traveling with constant speed might include a: • Yo-yo • Toy car on a track • Car on the highway with cruise control on • What does constant speed look like on a graph?
Exercise • Sketch a speed of 10 m/s on a x-vs-t graph • What is the slope (derivative) of the x-vs-t graph? • What if the graph is not constant? x (m) B D P C A t (s)
Instantaneous speed • Speed is the slope of the d-vs-t graph at a given point (a tangent line). • Which slope best represents the speed of the object at point P? • Instantaneous speed = the limit as ∆t 0 or ∆d or even better, dx ∆t dt
Calculus Break • The rate of change at an instantaneous point on a graph is called the derivative (it’s a tangent line). • Examples: dx (2t + 1) = 2 dx (t2) = 2t dtdt dx (41) = 0 dx (sin t) = cos t dtdt These are easily seen on a graph.
Velocity is expressed as a vector • Recall: • Add vectors tip to tail • Resultant vector is from start to finish • You may add vectors in any order (Commutative Property) • You can move vectors as long as you don’t • Rotate them • Change the length (magnitude)
More on velocity • Velocity, as a vector, has speed and direction • Same units as speed (m/s), just not a scalar • Average velocity: v = x t • Instantaneous velocity: v = dx dt
Pitfalls in this unit to watch out for! • Common intro error is to treat displacement, velocity, acceleration equal. They are NOT the same thing! • Use units to check. • Sign errors – signs indicate direction in vectors • Displacement ≠ distance
Calculus Break • Recall that integral calculus is the “undo-ing” of differential calculus. • So if the derivative of the x-vs-t graph is the speed of the object, then the integral (area under the curve) of the v-vs-t graph is the ____________.
Fundamental physics graphs we will use • x-vs-t • v-vs-t • a-vs-t • Each one above is the previous plot, differentiated • Each one above is the plot that follows, integrated This will make much more sense as we practice with them.
TIPERs – Work in small groups • NT3A-CT7 • NT3A-RT9 • NT3A-WWT10 • NT3A-QRT20 • NT3A-QRT21 • NT3A-WWT22
Exit Ticket • TIPER NT3A-WBT23 • Rip out of your packet and put your name on it. Put in the INBOX when you are finished. Show all work. • Should be done independently
