Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information.... 
Home Newtonian Physics Acceleration and Free Fall Examples Extracting acceleration from a graph  
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Extracting acceleration from a graph
The x  t and v  t graphs show the motion of a car starting from a stop sign. What is the car's acceleration? Acceleration is defined as the slope of the vt graph. The graph rises by 3 m/s during a time interval of 3 s, so the acceleration is (3 m/s)/(3 s) = 1 m/s^{2}. Incorrect solution #1: The final velocity is 3 m/s, and acceleration is velocity divided by time, so the acceleration is (3 m/s)/(10 s) = 0.3 m/s^{2}. The solution is incorrect because you can't find the slope of a graph from one point. This person was just using the point at the right end of the vt graph to try to find the slope of the curve. Incorrect solution #2: Velocity is distance divided by time so v = (4.5 m)/(3 s) = 1.5 m/s. Acceleration is velocity divided by time, so a = (1.5 m/s)/(3 s) = 0.5 m/s^{2}. The solution is incorrect because velocity is the slope of the tangent line. In a case like this where the velocity is changing, you can't just pick two points on the xt graph and use them to find the velocity.


Home Newtonian Physics Acceleration and Free Fall Examples Extracting acceleration from a graph 