![]() ![]() The average and instantaneous acceleration:.The average and instantaneous velocity:. ![]() The Introduction to Rectilinear Motion:.The acceleration-time graph looks like this:Ī brief description of the motion of the object could read something like this: At t = 0 s and object is stationary at some position and remains stationary until t = 2 s when it begins accelerating. During this time the gradient of the velocity-time graph is once again zero, and thus the object is not accelerating. its constant) throughout these 2 seconds so there must be a constant positive acceleration.įor the final 2 seconds the object is traveling with a constant velocity. (This makes sense because we know from the displacement time graph that the object is stationary during this time, so it can't be accelerating).įor the next 2 seconds the velocity-time graph has a positive gradient. Once we have the velocity-time graph its much easier to get the acceleration-time graph as we know that the gradient of a velocity-time graph is the just the acceleration.įor the first 2 seconds the velocity-time graph is horizontal at zero, thus it has a gradient of zero and there is no acceleration during this time. ![]() In this type of question it is just important to show whether velocities are positive or negative, increasing, decreasing or constant. Because we haven't been given any values on the vertical axis of the displacement-time graph, we cannot figure out what the exact gradients are and hence what the values of the velocity are. So our velocity-time graph looks like this one below. Thus, remembering that the gradient of a displacement-time graph is the velocity, the velocity must be increasing with time during this phase.įor the final 2 seconds we see that displacement is still increasing with time, but this time the gradient is constant, so we know that the object is now travelling at a constant velocity, thus the velocity-time graph will be a horizontal line during this stage. In fact, the slope is getting steeper (the gradient is increasing) as time goes on. Looking at the gradient of the displacement graph we can see that it is not constant. Thus the velocity during this time is zero and the object is stationary.įor the next 2 seconds, displacement is increasing with time so the object is moving. For the first 2 seconds we can see that the displacement-time graph is a horizontal line, i.e. We can reach this conclusion by another path too: remember that the gradient of a displacement-time graph is the velocity. The question explicitly gives a displacement-time graph.įor the first 2 seconds we can see that the displacement remains constant - so the object is not moving, thus it has zero velocity during this time. Step 1 : Analyse the question to determine what is given. Question: Given the displacement-time graph below, draw the corresponding velocity-time and acceleration-time graphs, and then describe the motion of the object. Worked Examples Worked Example 24 Relating displacement-, velocity-, and acceleration-time graphs Similarly, we can plot an acceleration-time graph from the gradient of the velocity-time graph.įigure 5.3: A Relationship Between Displacement, Velocity and Acceleration Given a displacement-time graph like the one on the left, we can plot the corresponding velocity-time graph by remembering that the slope of a displacement-time graph gives the velocity. Figure 5.3 shows how displacement, velocity and time relate to each other. Its useful to remember the set of graphs below when working on problems. We know the gradient (slope) of a graph is defined as the change in y divided by the change in x, i.e. This graphs shows us how, in 10 seconds time, the cyclist has moved from A to C. Below are some graphs that help us picture the concepts of displacement, velocity and acceleration.ĭisplacement-Time Graphs īelow is a graph showing the displacement of the cyclist from A to C: In physics we often use graphs as important tools for picturing certain concepts.
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