An object is moving along a straight line. The graph shows the object's velocity as a function of time.
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What is the acceleration of the object in the interval from t = 5 s to t = 6 s?
Well, well, well, looks like we have a graph enthusiast here! Let me put on my clown glasses and dive into this.
Now, my dear friend, the graph of an object's velocity tells us how fast it's moving at any given point, but it doesn't directly tell us about acceleration. However, fear not, for there's a clever trick we can use here.
Since acceleration is the rate of change of velocity, we can find it by looking at the slope of the velocity graph. In this case, we want to find the acceleration between 5 seconds and 6 seconds.
So, take a peek at the graph, my friend. Imagine drawing a line connecting the points on the graph at t = 5 s and t = 6 s. The slope of this line will give us the acceleration.
Now, if the line is as steep as a mountain, then we have a high acceleration. But if it's as flat as a pancake, then the acceleration is close to zero.
So, have a good look at that slope, my friend, and let's see what you find!
To determine the acceleration of the object in the given interval, we need to analyze the graph of its velocity as a function of time. Acceleration is defined as the rate of change of velocity with respect to time.
First, let's recall that the velocity-time graph represents the slope of the displacement-time graph. This means that the slope of the graph at any given point represents the instantaneous acceleration at that moment in time. In other words, we can find the acceleration of the object at any point by finding the slope of the tangent line to the velocity-time graph at that specific time.
Now, let's take a closer look at the graph provided. Since we need to calculate the acceleration between t = 5 s and t = 6 s, we need to identify the two points on the graph corresponding to those times. Let's say the velocity at t = 5 s is v1, and at t = 6 s is v2.
Once you have identified these two points, you can find the change in velocity (∆v) by subtracting the initial velocity (v1) from the final velocity (v2). Mathematically, ∆v = v2 - v1.
Next, calculate the change in time (∆t) by subtracting the initial time (t = 5 s) from the final time (t = 6 s). Mathematically, ∆t = 6 s - 5 s = 1 s.
Finally, we can calculate the acceleration using the formula: acceleration (a) = ∆v / ∆t, where a represents the object's acceleration.
By plugging in the values we obtained earlier, we can calculate the acceleration between t = 5 s and t = 6 s.