•The usual practice is to graph distance versus time, which puts distance on the vertical axis. •Note that the data points lie on a straight line.
1.4 Simple Types of Motion•Remember this simple rule for the relationship between distance and time: when the speed is constant, the graph of distance versus time is a straight line. •In general, when one quantity is proportionalto another, the graph of the two quantities is a straight line.
1.4 Simple Types of Motion•An important feature of this graph is its slope. •The slope of a graph is a measure of its steepness.•In particular, the slope is equal to the rise between two points on the line divided by the run between the points.
1.4 Simple Types of Motion•This is illustrated in the figure shown. •The rise is a distance, d, and the run is a time interval, t. •So the slope equals d divided by t, which is also the object’s velocity. •The slope of a distance-versus-time graph equals the velocity.
1.4 Simple Types of Motion•Even when the velocity is not constant, the slope of a d versus t graph is still equal to the velocity. •In this case, the graph is not a straight line because, as the slope changes (a result of the changing velocity), the graph curves or bends.•Indicates acceleration.
1.4 Simple Types of Motion•The graph shown represents the motion of a car that starts from a stop sign, drives down a street, and then stops and backs into a parking place.aVsTime/xVsTime.htmlInteractive tool – position vs. time graph
1.4 Simple Types of MotionConstant Acceleration•Let’s use free fall as our example. •Assume that a heavy rock is dropped from the top of a building and that we can measure the instantaneous velocity of the rock and the distance that it has fallen at any time we choose. •The rock falls with an acceleration equal to g = 9.8 m/s2
1.4 Simple Types of MotionConstant Acceleration
1.4 Simple Types of MotionConstant Acceleration•First, consider how the rock’s velocity changes. The velocity increases 9.8 m/s, each second. •Mathematically, v (m/s)= 9.8 (m/s2) x t (s)The general form of the equation that applies to any object that starts from rest and has a constant acceleration a is v = at (when acceleration is constant)
1.4 Simple Types of MotionConstant Acceleration•Review: the graph of distance versus time is a straight line for constant velocity (uniform motion). •For constant acceleration, the graph of velocity versus timeexhibits a linear behaviour.
1.4 Simple Types of MotionConstant Acceleration•What is the relationship between distance and time when the acceleration is constant? •It is a bit more complicated, as expected. •The figure shows that the distance a falling body travels during each successive time interval grows larger as it falls. •Because the velocity is continually changing, the distance equals the average velocity multiplied by the time.
1.4 Simple Types of MotionConstant Acceleration•What is the average velocity?