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max2010maxim [7]
3 years ago
7

A car start from rest and accelerates at the rate of 2m/s² for 5 seconds. it maintenance this velocity for another 5 seconds. it

eventually undergoes a uniform deceleration and finally comes to rest after further 5 seconds.
A) draw the velocity-time graph for the journey

B) find the acceleration and deceleration respectively,

C) find the total distance travelled during each stage.

D) find the average velocity over the entire period ​
Mathematics
1 answer:
Vladimir79 [104]3 years ago
5 0

Answer:

2m/s² ; - 2m/s²

25m ; 50m ; 25m

6.67 m/s²

Step-by-step explanation:

The acceleration and deceleration :

Both rates are the Same from the graph ;

According to scenario described, acceleration = 2m/s²

Deceleration occurred in equal time interval = - 2m/s

Distance covered during each stage:

Stage 1 : area of triangle

0.5 * base * height

0.5 * 5 * 10 =25 m

Stage 2: area of rectangle :

Length * breadth = 5 * 10 = 50 m

Stage 3 : area of triangle

0.5 * base * height

0.5 * 5 * 10 =25 m

Average Velocity :

Total distance / time = (25 + 50 + 25) / 15 = 100/ 15 = 6. 67 m/s

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Answer:

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3 years ago
The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral
Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have y_4 - y_3 so one side is CD. The other side must be BC or AD; AD would give y_4 - y_1 terms which don't appear among the answer, so let's go with BC.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

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Look here in a square which is what I imagine that drawing is all the angles are 90 degrees. A rectangle would be knowing two angles is know all of them one way or another so fix your work and you should know the answer

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