![]() ![]() We can now take these values and sub them into this equation to calculate the force □ that’s applied to the object. So, we know the mass □ of the object, and we have now found the object’s acceleration □. Then, evaluating the expression, we find that □ is equal to 2.48 meters per second squared. Subbing in our values gives us that □ is equal to 12.4 meters per second divided by five seconds. This lets us calculate the slope of the graph, which gives us the acceleration □ of the object. ![]() We can now sub these values for Δ□ and Δ□ into this expression. This gives us that Δ□ is equal to 12.4 meters per second. Then, the change in velocity Δ□ between the two points on the graph is equal to 12.4 meters per second, that’s the velocity at the right-hand point, minus zero meters per second, the velocity at the left-hand point. This gives it a value of 12.4 meters per second. This height is one-fifth of the way between the 12 meters per second mark and the next mark, which would be 14 meters per second. Then, looking now at the right-hand point, we see that it traces across to this height on the velocity axis. ![]() We can see that the left-hand point has a velocity value of zero meters per second. This gives us that Δ□ is equal to five seconds. The change in the time value between this point and this point on the graph, which is Δ□, is equal to five seconds, so that’s the time value at the right-hand point, minus zero seconds, the time value at the left-hand point. Meanwhile, tracing down from the right-hand point until we get to the time axis, we see that this point has a time value of five seconds. ![]() We can see that the left-hand point is at a time value of zero seconds. So, that’s this point here on the left and this point on the right. We’ll consider the two points that are right at the ends of the graph. So, let’s work out the value of □ by finding the slope of this velocity–time graph. This means that if we can work out the value of the acceleration □, then we have all of the information that we need to calculate the force applied to the object. So, in this equation, we know the value of □. The question tells us that the mass of the object is 75 kilograms. This is often written in terms of symbols as force □ is equal to mass □ multiplied by acceleration □. This says that the force applied to an object is equal to the object’s mass multiplied by its acceleration. The reason for this is Newton’s second law of motion. However, we’re going to see that it will be useful to first find this acceleration in order to then work out the force. Now, the question isn’t actually asking us to find the acceleration, but rather the force that is applied to the object. This means that the acceleration □ of an object is equal to the slope of that object’s velocity–time graph. And the rate of change of velocity will be equal to the change in velocity divided by the change in time over which that velocity change occurs. We can recall that the acceleration of an object is equal to the rate of change of that object’s velocity. And so, the slope of the graph, which is defined as the change in the vertical coordinate divided by the change in horizontal coordinate, is equal to the change in velocity, Δ□, divided by the change in time, Δ□. The graph plots velocity on the vertical axis against time on the horizontal axis. This question gives us a graph, and that graph shows the change in an object’s velocity while a force is applied to it. How much force is applied to the object? Give your answer to the nearest newton. The graph shows the change in the object’s velocity while the force is applied. An object of mass 75 kilograms has a force applied to it. ![]()
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