A cat walks in a straight line, which we shall call the x -axis with the positiv
ID: 2125786 • Letter: A
Question
A cat walks in a straight line, which we shall call the x-axis with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time.
What distance does the cat move from t=0 to t=7.5s?
Answer: 26cm.
The solution can be found by computing displacement for t: [0,6] and t: [6,7.5] seperately.
My question is, when doing so, why do we use a negative acceleration for the first part of the graph (t: [0,6]) and then a positive acceleration for the second part (t: [6,7.5])?
Solution:
t: [0,6] 24.06 = 8*6+ 0.5(-1.33)(6^2)
t: [6,7.5] 1.5 = 0(1.5)+ 0.5(1.33)(1.5^2)
Accleration is still a constant negative. So why do we use a positive in the second equation? Using a negative acceleration would yield an answer of 24-1.5 = 22.5cm. But the answer is 24+1.5 = 26cm.
This is driving me insane. Please exlpain.
Explanation / Answer
Very easy.
Slope = 8/6 = 4/3
distance covered in first 6 seconds = area under curve = 1/2 * 8*6 = 24 cm
distance covered in next 1.5 sec i.e. from 6 sec to 7.5 sec is area under the other part
Area = 1/2 * 1.5 * x
Similar triangles: x/1.5 = 8/6
=> x = 2
=> Area = 1/2 * 3/2 * 2 = 1.5cm
So the answer comes 25.5 = 26cm
Now coming to ur problem.
We use that equation for calculating the displacement and not the distance travelled
If u travel 2cm forward and 2 backward then net displacement is zero but distance is 2
Displacement = (+2) + (-2) = 0
But distance = |+2| + |-2| = 4
So in the eqaution for negative acceleration ur displacemenet comes out to be negative hence for distance purpose add it as positive quantity.
Please rate if it helps.