Position, velocity, and acceleration
RELATIONSHIPS BETWEEN. POSITION, VELOCITY, AND ACCELERATION. Velocity, v(t), is the rate of change of position, s(t) ' v t s t.. Acceleration. It does not deal with the sources of their motion; we'll discuss dynamics in a few weeks. Displacement is a vector which points from the initial position of an object to Instantaneous velocity, on the other hand, describes the motion of a body at . First, position has the same relationship with velocity that velocity has with .. What is the relation between initial velocity, acceleration, and time in a uniformly .
Logger Lite free download: If necessary, guide the class discussion so that students reach this understanding. In order to complete the associated activity, "Gaitway" to Acceleration: Walking Your Way to Accelerationstudents must understand what a secant line to a curve is and how to compute Riemann sums. So, teach students the following lesson content to prepare them for the associated activity. A secant line of a curve is a line that intersects a curve in a local region at two points on the curve.
As the two intersection points become closer together on the curve, the secant line becomes closer and closer to the tangent line at a point on the curve.
In calculus, the derivative evaluated at a point on the curve is the slope of the tangent line at that evaluated point. A secant line is a way to approximate derivatives without taking a derivative. In the associated activity, the data does not have a corresponding equation although you could perform a regression to find one so taking a derivative is not possible.
Position, Velocity and Acceleration - Lesson - TeachEngineering
Secant lines allow the approximation of the derivative which would represent the velocity of the object without requiring the computation of the derivative. If you create a curve from the associated points found by taking a derivative or approximating using secant linesyou can create a velocity curve of the object.
Computing secant lines for this curve in the same fashion as the previous example is a method for approximating the second derivative, which represents the acceleration of the object. Again, by using secant lines, the acceleration can be approximated without having an equation and using calculus.
To compute a secant line, select two points, calculate the slope, plug one of the selected points and the slope into point slope form, and then algebraically manipulate it into any form of the line that you wish. When working from the object's position, the secant line evaluated at an appropriate "x" value yields a "y" value that represents the object's velocity first derivative. When working from the object's velocity, the secant line evaluated at an appropriate "x" value yields a "y" value that represents the object's acceleration second derivative.
A Riemann sum is an approximation of the area under a curve. The sum is computed by dividing the region into polygons rectangles, trapezoids, etc. The area for each of the polygons is computed using an appropriate area equation and the results are added to approximate the region. Using Riemann sums, a numerical approximation of a definite integral can be found.
Similar to the secant line, a Riemann sum can be used to approximate an object's velocity or position without having an equation that you can integrate. An integral is the inverse of a derivative. Hence, a Riemann sum approximation works backwards from a secant line approximation.
Equations of Motion
Given an object's acceleration curve, a Riemann sum can be used to determine an object's velocity curve. Given an object's velocity curve for an object, a Riemann sum can be used to determine an object's position curve.
Various Definitions of Acceleration In recognizable terms: In common words, acceleration is a measure of the change in speed of an object, either increasing acceleration or decreasing deceleration. Take the case of the meteor. What velocity is represented by the symbol v? If you've been paying attention, then you should have anticipated the answer. It could be the velocity the meteor has as it passes by the moon, as it enters the Earth's atmosphere, or as it strikes the Earth's surface.
Displacement, velocity, acceleration
It could also be the meteorite's velocity as it sits in the bottom of a crater. Are any of these the final velocity?
Someone could extract the meteorite from its hole in the ground and drive away with it. Probably not, but it depends.
There's no rule for this kind of thing. You have to parse the text of a problem for physical quantities and then assign meaning to mathematical symbols. The last part of this equation at is the change in the velocity from the initial value. Recall that a is the rate of change of velocity and that t is the time after some initial event.
Rate times time is change. Move longer as in longer time. Acceleration compounds this simple situation since velocity is now also directly proportional to time.
Try saying this in words and it sounds ridiculous.Position Velocity & Acceleration Time Graphs, Physics, Graphical Analysis of Linear Motion
Would that it were so simple. This example only works when initial velocity is zero.