Unit Kinematics Module Investigating One Dimensional Motion page 1 of 1 Another Look at Position Velocity and Acceleration The derivative of position with respect to time is velocity The derivative of velocity with respect to time is acceleration To find the velocity from the acceleration you need to know the velocity at one point in time The acceleration tells you the slope of the velocity function The top graph is the position function of a ball tossed in the air The equation for the ball s path is a parabola with a maximum at t 2 s x 5t 2 20t The velocity of the ball is shown in the second graph Its equation is the derivative with respect to time of the position function v 10t 20 Initially the velocity of the ball is large and in the positive direction The velocity is zero at the highest point in the ball s path t 2 s As the ball falls back to the ground the magnitude of the velocity increases but the ball moves in the negative direction The ball s acceleration is shown in the bottom graph Its equation is the derivative of the velocity function with respect to time a 10 The acceleration of the ball is constant and it is always negative or towards the ground An object s position velocity and its acceleration are shown in the top center and bottom graph respectively During the first half of a second the object moves in the negative direction Then the object it turns and moves in the positive direction Its velocity is initially large and negative At 0 5 s the object s velocity is zero Between 0 5 and 1 s its velocity is positive and increasing The acceleration of the object is constant and positive during the entire first second During the time period between 1 and 2 s the object moves linearly in the positive direction Because the object s movement is uniform its velocity is constant and its acceleration is zero During the last two seconds the object continues moving in the positive direction but slows down Its velocity linearly decreases to nearly zero The object s acceleration is constant and negative during this time period www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1800 rev 03 19 2001
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