Movement and Position

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1 Movement and Position

2 Syllabus points: 1.2 plot and interpret distance-time graphs 1.3 know and use the relationship between average speed, distance moved and 1.4 describe experiments to investigate the motion of everyday objects such as toy cars or tennis balls 1.5 know and use the relationship between acceleration, velocity and time: 1.6 plot and interpret velocity-time graphs 1.7 determine acceleration from the gradient of a velocity-time graph 1.8 determine the distance travelled from the area between a velocity-time graph and the time axis.

3 distance (m) distance (m) Syllabus points: 1.2 plot and interpret distance-time graphs You need to be able to plot accurate distance-time graphs. Skills tested here will include: plotting points accurately labelling axes with quantities and units selecting an appropriate scale (filling over half the page, avoiding weird scales) Distance-time graphs and velocity-time graphs are some of the only graphs in physics where you connect the points dot-to-dot. The shape of a distance-time graph helps describe the motion of the object. At rest A flat line shows that the object s distance is not changing; i.e. they are not moving/they are stationary. The gradient of a distance time graph tells you the average speed between the two points in the time selected. This is because the of a flat line is zero, the speed is zero.. As the gradient Constant speed A straight line shows that the object is travelling the same amount of distance each second; i.e. they are moving at a constant speed. The gradient of a distance time graph tells you the average speed between the two points in the time selected. This is because the. As the gradient of a straight line is constant, the speed is constant. A steeper gradient means a greater (i.e. faster) speed.

4 distance (m) Increasing speed A curved line represents a change in speed. This could be an increase (acceleration) or a decrease (deceleration). If the gradient of the line is increasing (shallow to steep) then the speed is increasing (acceleration); if the gradient of the line is decreasing (steep to shallow) then the speed is decreasing (deceleration). The gradient of a distance time graph tells you the average speed between the two points in the time selected. This is because the. 1.3 know and use the relationship between average speed, distance moved and Speed is defined as how far an object travels in a given time. You are probably used to the speed of cars being measured in miles per hour (i.e. how many miles you would travel if you moved at that speed for a whole hour). So travelling at 60 mph you would move 30 miles in half an hour and 120 miles in 2 hours. In physics we use the metric system, so the standard units for the quantities are: distance moved; metres, m time taken; seconds; s average speed; metres per second; m/s There are two categories of speed; average speed and instantaneous speed. Both have a very similar equation;

5 distance (m) This makes a little more sense when comparing 2 objects moving the same distance in the same time Constant speed Slow then fast In the graph above the blue line (top line) has the same gradient throughout and shows the object moving as a constant speed. We can find the speed of this by finding the gradient. In this case 50 m/10 s = 5 m/s. The red line (lower line) has 2 distinct gradients; for the first 5 seconds the object travels 10 m so has an instantaneous speed of 10 m/5 s = 2 m/s. In the next 5 s it travels 40 m so has an instantaneous speed of 40 m/5 s = 8 m/s. However, they have still travelled a total of 50 m in 5 s so their average speed is 50 m/ 10s = 5 m/s. 1.4 describe experiments to investigate the motion of everyday objects such as toy cars or tennis balls How would you go about investigating the motion of an everyday object? This could be a toy car on a slope or a ball rolling along a surface. 1) You could measure out the distance between 2 points using a ruler, mark these points with some sort of marker. Then start the stopwatch when the object passes the first marker. Stop the stopwatch when it goes past the second marker. You should repeat this a couple of times to ensure that you are collecting consistent data. To find the average speed of everyday object you just need to divide the distance between markers by the average time measured on the stopwatch. 2) The next method uses light gates and works in a similar way; set up two light gates so that the everyday object passes through both. Light gates consist of a beam of light and a detector. When the beam of light is broken by something this sends a signal to a computer or datalogger. Measure the distance between these light gates with a ruler. When the everyday object passes through the first light gate the computer or datalogger it is conneted to will start a stopwatch. When the everyday object passes through the second light gate the stopwatch will be stopped. Again you can find the average speed by dividing the distance between light gates by the average time taken.

6 3) The next method is to use a high speed camera and markers in the scene. Measure out a distance and mark with cone markers again. Video the everyday object moving past the two cones. Watch back the video and look at the time when the everyday object goes past the first cone. Let the video continue playing and then look at the time when it reaches the second cone. Then do the distance measured divided by time taken to get average speed. 4) The final method is to use a ticker tape timer. This device marks a dot every 0.02 s on a piece of ticker tape (thin piece of paper). The other end of the ticker tape is attached to the everyday object. Once the everyday object has moved the ticker tape is processed. This involves marking a dot and then moving on 5 more dots; this represents 0.1 s of travel (5 x 0.02 s = 0.1 s). The speed of the everyday object is equal to the length covered by 5 dots divided by 0.1 s. 5cm Above, each section of 5 dots (which represent 0.1 s of travel) are the same length; this means the everyday object is travelling at a constant speed. In this example the everyday object is moving at 5 cm/0.1 s = 50 cm/s Above, the distance between dots has increased; however, the time between dots is still the same. This means the everyday object is moving further in the same amount of time; i.e. it is accelerating. Above, the distance between the dots has decreased; however, the time between dots is the same. This means the everyday object is moving less far in the same amount of time; i.e. it is decelerating. 1.5 know and use the relationship between acceleration, velocity and time: Acceleration is the rate of change of velocity (remember that rate in physics means per unit time so acceleration is the change in velocity per second). The unit for acceleration is m/s 2 or m/s/s. This is because it is the change in velocity (m/s) per second (/s) i.e. metres per second per second. Velocity is essentially speed in a given direction (for example a velocity of 5 m/s would mean moving down at a speed of 5 m/s). We ll look more at this in another set of notes. For now, don t worry too much about it.

7 velocity (m/s) velocity (m/s) Change in velocity is equal to the final velocity (v) minus the initial velocity (u). For example if a car accelerates from 10 m/s to 20 m/s in 5s the acceleration will be:. If the change in velocity is negative then the acceleration will be negative i.e. a deceleration. For example if a car brakes from 30 m/s to 10 m/s in 4 s the acceleration will be. This is equal to a deceleration of 5 m/s plot and interpret velocity-time graphs You need to be able to plot accurate velocity-time graphs. Skills tested here will include: plotting points accurately labelling axes with quantities and units selecting an appropriate scale (filling over half the page, avoiding weird scales) Distance-time graphs and velocity-time graphs are some of the only graphs in physics where you connect the points dot-to-dot. The shape of a velocity-time graph helps describe the motion of the object. Stationary This velocity-time graph shows the velocity remains at zero. This means the object is not moving. time Constant velocity A flat line shows that the object s velocity is not changing; i.e. they are moving with a constant velocity. The gradient of a velocity-time graph tells you the acceleration between the two points in time selected. This is because the is zero, the acceleration is zero. time. As the gradient of a flat line

8 velocity (m/s) velocity (m/s) Constant acceleration A straight line shows that the objects velocity is changing at a constant rate; i.e. they are accelerating with a constant acceleration. The gradient of a velocity-time graph tells you the acceleration between the two points in time selected. This is because the. As the gradient of a straight line is constant, the acceleration is constant. Increasing acceleration A curved line shows that the object s acceleration is changing. If the gradient of the line is increasing (shallow to steep)_then the rate of acceleration is increasing; in the much more common case of the gradient of the line decreasing (steep to shallow) then the acceleration is decreasing. The gradient of a velocity-time graph tells you the acceleration between the two points in time selected. This is because the.

9 velocity (m/s) velocity (m/s) You may be asked to describe the shape of a velocity time graph; it is important that you focus on the shape. Consider the following example: The gradient is initially steep. Then it flattens out to a horizontal line. Finally the gradient increases again but to a lesser gradient than during the first part of the graph. The motion that this represents is an object accelerating with a high constant acceleration, then moves at a constant velocity, then accelerates again but with a lower acceleration. 1.7 determine acceleration from the gradient of a velocity-time graph As discussed above, A positive (sloping upwards) gradient shows an acceleration. A negative (sloping downwards) gradient shows deceleration. 1.8 determine the distance travelled from the area between a velocity-time graph and the time axis. The area between a velocity-time graph and the time axis is equal to velocity time which is the distance travelled. This is sometimes known as the area under a graph. The orange line is the velocity-time graph line. The blue shaded area represents the area under the graph / area between the velocity-time graph and the time axis. This means the area of the blue shapes is equal to the distance travelled.

10 velocity (m/s) part 1 part In the example above it is easier to split the objects journey into 2 parts: In part one the object is accelerating with a constant acceleration of (as this is the gradient of the line). The area under the graph is equal to ½ x 40 s x 20 m/s (area of a triangle ½ base height). This means that during the accelerating stage of the journey the object has moved 400 m. In part two the object is moving with a constant velocity (flat line, no acceleration). The area under the graph is equal to 20 m/s 20 s = 400 m. (Care needs to be taken here as the time between 40 s and 60 s is 20 s). The total distance travelled is 800 m. The average speed for this journey would be 800 m/60 s = 13.3 m/s. This means an object travelling at 13.3 m/s would arrive at the end point at the same time as the object in the graph.

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