What is the slope of the graph?
1 answer:
<u>Given</u>:
Given that an aquarium is being filled with water.
The given graph shows the height of the water over time as the aquarium is being filled.
We need to determine the slope of the graph.
<u>Slope</u>:
The slope of the given graph can be determined using the formula,
Since, the slope is same for all the points on the straight line, then let us consider the points (2,5) and (4,10)
Substituting these points in the above formula, we get;
Simplifying, we get;
Thus, the slope of the given graph is 2.5
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Answer:
-18
Step-by-step explanation:
Hope it helps....................................................
a(i). Since you are given a velocity v. time graph, the distance will be represented by:
In this case, however, we can just use simple geometry to evaluate the area under the graph v(t). I split it up into 2 trapezoids, and 1 rectangle. So, the area will be as follows:
So, the particle traveled a total of 1275m assuming it never turned back (because it says to calculate distance).
a(iii). Deceleration is a word for negative acceleration. Acceleration is the first derivative of velocity, and so deceleration is too. So, we just need to find the slope of the line that passes through t = 30 because it has a linear slope (meaning the slope doesn't change). So, we can just use simple algebra instead of calculus to figure this out. Recall from algebra that slope (m):
So, let's just pick values. I'm going to pick (25, 30) and (35, 15). Let's plug and chug:
Since it's a negative value, this means that acceleration is negative but deceleration is positive (because deceleration is negative acceleration). So, your answer is: The deceleration of the particle at t = 30s is 3/2 or 1.5.
In this case, however, we can just use simple geometry to evaluate the area under the graph v(t). I split it up into 2 trapezoids, and 1 rectangle. So, the area will be as follows:
So, the particle traveled a total of 1275m assuming it never turned back (because it says to calculate distance).
a(iii). Deceleration is a word for negative acceleration. Acceleration is the first derivative of velocity, and so deceleration is too. So, we just need to find the slope of the line that passes through t = 30 because it has a linear slope (meaning the slope doesn't change). So, we can just use simple algebra instead of calculus to figure this out. Recall from algebra that slope (m):
So, let's just pick values. I'm going to pick (25, 30) and (35, 15). Let's plug and chug:
Since it's a negative value, this means that acceleration is negative but deceleration is positive (because deceleration is negative acceleration). So, your answer is: The deceleration of the particle at t = 30s is 3/2 or 1.5.