Motion at Constant Acceleration, Grade 10 Physics The final situation we will be studying is motion at constant acceleration. We know that acceleration is the rate of change of velocity. So, if we have a constant acceleration, this means that the velocity changes at a constant rate. Let’s look at our first example of Lesedi waiting at the taxi stop again. A taxi arrived and Lesedi got in. The taxi stopped at the stop street and then accelerated as follows: After 1 s the taxi covered a distance of 2,5 m, after 2 s it covered 10 m, after 3 seconds it covered 22,5 m and after 4 s it covered 40 m. The taxi is covering a larger distance every second. This means that it is accelerating. To calculate the velocity of the taxi you need to calculate the gradient of the line at each second: From these velocities, we can draw the velocity-time graph which forms a straight line. The acceleration is the gradient of the v vs. t graph and can be calculated as follows: The acceleration does not change during the motion (the gradient stays constant). This is motion at constant or uniform acceleration. The graphs for this situation are shown in Figure 3.9. Velocity from Acceleration vs. Time Graphs Just as we used velocity vs. time graphs to find displacement, we can use acceleration vs. time graphs to find the velocity of an object at a given moment in time. We simply calculate the area under the acceleration vs. time graph, at a given time. In the graph below, showing an object at a constant positive acceleration, the increase in velocity of the object after 2 seconds corresponds to the shaded portion. The velocity of the object at t = 2 s is therefore 10 m·s-1. This corresponds with the values obtained in Figure 3.9. Exercise: Graphs E - 1. A car is parked 10 m from home for 10 minutes. Draw a displacement-time, velocity-time and acceleration-time graphs for the motion. Label all the axes. E - 2. A bus travels at a constant velocity of 12 m·s-1 for 6 seconds. Draw the displacement-time, velocity-time and acceleration-time graph for the motion. Label all the axes. E - 3. An athlete runs with a constant acceleration of 1 m·s-2 for 4 s. Draw the acceleration-time, velocity-time and displacement time graphs for the motion. Accurate values are only needed for the acceleration-time and velocity-time graphs. E - 4. The following velocity-time graph describes the motion of a car. Draw the displacement-time graph and the acceleration-time graph and explain the motion of the car according to the three graphs. E - 5. The following velocity-time graph describes the motion of a truck. Draw the displacement-time graph and the acceleration-time graph and explain the motion of the truck according to the three graphs. Xem thêm: Physics 10.II Motion in One Dimension High School Students Studying the Sciences Physics