Then draw a few velocity graphs and see if they can get the corresponding position graph. Students should then be able to see that the corresponding velocity graph is a horizontal line at 0.5km/minute and then a horizontal line at –0.5 km/minute. Ask the students what the velocity is at different times on that graph. Return to the scenario of the drive to and from school.
At the beginning of the motion, as the car is speeding up, we saw that its position is a curve, as shown in Figure 2.17. īut what if the velocity is not constant? Let’s look back at our jet-car example. And in this graph, the y-intercept is v 0. As we said, the slope equals the acceleration, a. time graph, we can also define one for a velocity vs. Just like we could define a linear equation for the motion in a position vs. For now, just remember that the area under the graph and the slope are the two important parts of the graph. We will do more with this information in a later chapter. This slope tells us that the car is not speeding up, or accelerating. Graphically, you can see that the slope of these two lines is 0. In our earlier example, we stated that the velocity was constant. The velocity curve also tells us whether the car is speeding up. The area under a velocity curve represents the displacement. This process is called dimensional analysis, and it is one of the best ways to check if your math makes sense in physics.
For instance, if we end up with m × s for velocity instead of m/s, we know that something has gone wrong, and we need to check our math. This is good because it can tell us whether or not we have calculated everything with the correct units. You can treat units just like you treat numbers, so a km/km=1 (or, we say, it cancels out). If we add them together, we see that the net displacement for the whole trip is 0 km, which it should be because we started and ended at the same place. If we calculate the same for the return trip, we get –5 km. The units for minutes cancel each other, and we get 5 km, which is the displacement for the trip to school. Let’s take just the first half of the motion. In Figure 2.16, we have velocity on the y-axis and time along the x-axis. If we use a little algebra to re-arrange the equation, we see that d = v × × t. time graph to determine velocity, we can use a velocity vs. There are a few other interesting things to note. Second, if we have a straight-line position–time graph that is positively or negatively sloped, it will yield a horizontal velocity graph. First, we can derive a v versus t graph from a d versus t graph. The area between the curve and the time axis of a velocity–time or a speed–time graph represents the distance travelled.Ĭheck that the shaded area represents a distance of 11.25 m in each case.Figure 2.16 Graph of velocity versus time for the drive to and from school. The gradient of a velocity–time graph represents the acceleration. Remember, the area of a triangle = 1?2 × base × height. The area that represents the distance travelled by the ball while moving upwards is shaded on each graph. Since distance travelled = average speed × time, this is represented by the area between the curve and the time axis. The distance that the ball travels in any time interval can also be obtained from the graphs. In each case the gradient of the graph is numerically equal to the acceleration (as the ball is moving vertically this is free-fall acceleration), but the gradient of the velocity–time graph also shows that the direction of the acceleration (vertically downwards) is opposite to that of the initial velocity. The velocity–time graph also shows the change in direction of the ball. The speed–time graph shows that the speed decreases to zero as the ball reaches its maximum height and then increases. The graphs below both represent the motion of a ball after it has been thrown vertically upwards with an initial speed of 15 m s –1. Speed–time and velocity–time graphs both give information about the motion of an object that is accelerating. This means that an object moving at constant speed, but changing direction, is accelerating. In physics, any change in velocity is an acceleration. It is represented by the gradient of a velocity–time graph.Īverage acceleration = change in velocity ÷ time a = Δv ÷ ΔtĪcceleration is a vector quantity and is measured in m s –2. Instantaneous acceleration = rate of change of velocity. Acceleration is a measure of how quickly the velocity of an object changes.
Speeding up, slowing down and going round a corner at constant speed are all examples of acceleration. Any object that is changing its speed or direction is accelerating.
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