2 One-Dimensional Motion Examples:a car moving on a straight roada person walking down a hallwaya sprinter running on a straight race coursedropping a pencilthrowing a ball straight upa glider moving on an air trackand many others...
3 DerivativesThe position graph s(t), where x is time and the y is distanceThe velocity graph v(t), is the derivative of the position graph, based on how quickly the distance is changingThe acceleration graph a(t), is the derivative of the velocity graph, based on how quickly the velocity is changing
4 Position This graph records the distance that is travel Let’s use the example of a person that is walkingthe distance either increases or decreases relative to where the starting point is but to make things easier right (forward) is positive and left (backward) is negative
5 Velocitythis graph based on the slope of the position graph meaning how slow or how fast the person is travelingA positive slope – the person is walking to the right and the distance is increasingAn increase in the positive slope - the person is walking faster so the distance is increasing at a faster rateA decrease in the positive slope – the person is walking slower so the distance is increasing at a slower rateZero slope – the person has walking and no distance has been traveled
6 Cont.Zero slope – the person has stopped and no distance has been traveledA negative slope - the person is walking in the negative direction (left) so the distance is decreasingAn increase in the negative slope – the person is walking faster in the left direction so the distance is decreasing at a faster rateAn decrease in the negative slope – the person is walking slower in the left direction so the distance is decreasing at a slower rate
7 AccelerationThis graph is based on the slope of the velocity meaning how fast or how slow the person is changing his paceFor example : walking to walking faster as opposed to walking to runninga positive slope – the person changes from walking to running, increasing the pace of its travel at a exponential pattern (3 ft/sec to 9 ft/sec to 81 ft/sec)Zero slope – the person changes from walking to walking faster at a consistent pattern (2 ft/sec to 4 ft/sec to 6 ft/sec)a negative slope – the person changes from running to walking, decreasing the pace of its travel at an exponential pattern (81 ft/sec to 9 ft/sec to 3 ft/sec)