The slope of the curve is positive between the times t=0\text{ s}t=0 st, equals, 0, start a text, space, s, end text, and t=2 \text{ s}t=2 st, equals, 2, start a text, space, s, end text since the slope is directed upward. This means the acceleration is positive.
The slope of the curve is negative between t=2 \text{ s}t=2 st, equals, 2, start a text, space, s, end text, and t=8 \text{ s}t=8 st, equals, 8, start a text, space, s, end text since the slope is directed downward. This means the acceleration is negative.
At t=2\text{ s}t=2 st, equals, 2, start a text, space, s, end text, the slope is zero since the tangent line is horizontal. This means the acceleration is zero at that moment.
Concept check: Is the object whose motion is described by the graph above speeding up or slowing down at time t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text?
[Show me the answer.]
What does the area under a velocity graph represent?
The area under a velocity graph represents the displacement of the object. To see why to consider the following graph of motion that shows an object maintaining a constant velocity of 6 meters per second for a time of 5 seconds.
To find the displacement during this time interval, we could use this formula
\Delta x=v\Delta t=(6\text{ m/s})(5\text{ s})=30\text{ m}Δx=vΔt=(6 m/s)(5 s)=30 mdelta, x, equals, v, delta, t, equals, left parenthesis, 6, start text, space, m, slash, s, end text, right parenthesis, left parenthesis, 5, start text, space, s, end text, right parenthesis, equals, 30, start text, space, m, end text
which gives a displacement of 30\text{ m}30 m30, start text, space, m, end text.
Now we're going to show that this was equivalent to finding the area under the curve. Consider the rectangle of the area made by the graph as seen below.
The area of this rectangle can be found by multiplying the height of the rectangle, 6 m/s, times its width, 5 s, which would give
\text{ area}=\text{height} \times \text{width} = 6\text{ m/s} \times 5\text{ s}=30\text{ m} area=height×width=6 m/s×5 s=30 mstart text, space, a, r, e, a, end text, equals, start text, h, e, i, g, h, t, end text, times, start text, w, i, d, t, h, end text, equals, 6, start text, space, m, slash, s, end text, times, 5, start text, space, s, end text, equals, 30, start text, space, m, end text
This is the same answer we got before for the displacement. The area under a velocity curve, regardless of the shape, will equal the displacement during that time interval. [Why is this still true when velocity isn't constant?]
\text{area under curve}=\text{displacement}area under curve=displacementstart text, a, r, e, a, space, u, n, d, e, r, space, c, u, r, v, e, end text, equals, start text, d, i, s, p, l, a, c, e, m, e, n, t, end text
[Wait, aren't areas always positive? What if the curve lies below the time axis?]
What do solved examples involving velocity vs. time graphs look like?
Example 1: Windsurfing speed change
A windsurfer is traveling along a straight line, and her motion is given by the velocity graph below.
Select all of the following statements that are true about the speed and acceleration of the windsurfer.
(A) Speed is increasing.
(B) Acceleration is increasing.
(C) Speed is decreasing.
(D) Acceleration is decreasing.
Options A, speed increasing, and D, acceleration decreasing, are both true.
The slope of a velocity graph is the acceleration. Since the slope of the curve is decreasing and becoming less steep this means that the acceleration is also decreasing.
It might seem counterintuitive, but the windsurfer is speeding up for this entire graph. The value of the graph, which represents the velocity, is increasing for the entire motion shown, but the amount of increase per second is getting smaller. For the first 4.5 seconds, the speed increased from 0 m/s to about 5 m/s, but for the second 4.5 seconds, the speed increased from 5 m/s to only about 7 m/s.
Example 2: Go-kart acceleration
The motion of a go-kart is shown by the velocity vs. time graph below.
A. What was the acceleration of the go-kart at time t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text?
B. What was the displacement of the go-kart between t=0\text{ s}t=0 st, equals, 0, start text, space, s, end text and t=7\text{ s}t=7 st, equals, 7, start text, space, s, end text?
A. Finding the acceleration of the go-kart at t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text
We can find the acceleration at t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text by finding the slope of the velocity graph at t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text.
\text{slope}=\dfrac{\text{rise}}{\text{run}}slope=
run
Math question! I don't understand! can I have an explanation?
Answer:
linear monomial
Step-by-step explanation:
help me with is please the question is in the picture
Answer: the answer is b or 6.48
Step-by-step explanation:
Solve for the bottom please!!! Only if you know!
Answer:
aproximately 23.5 I believe
Step-by-step explanation:
ok, so first you square 17, which is 289. then you square 29, which is 841. subtract 289 from that:
841-289=552
now take the square root of 552
aproximately 23.5 I believe
Answer: 23cm
Step-by-step explanation:
a² + b² = c²
x² + 17² = 29²
x² + 289 = 841
x² = 552
√x² = √552
x ≈ 23 cm
Find the volume of a pyramid with a square base, where the area of the base is 7.5cm^2
and the height of the pyramid is 8.6cm. Round your answer to the nearest tenth of a cubic centimeter.
Answer:
21.5 cu. cm.
Step-by-step explanation:
Volume of a pyramid is
V = 1/3Bh B = area of the base h = height of pyramid
V = 1/3(7.5)(8.6)
= 21.5 cu. cm.
Verify that ABC ~ DEF. Find the scale factor of ABC to DEF.
Answer:
ABC and DEF are both similar triangles, this is because, the ratio of their corresponding sides are equal. The scale factor 3/2 ( Which means that each side of the triangle ABC is 3/2 times greater than each of the sides of the triangle DEF
what is -2 to the 8th power
Answer:
-256
Step-by-step explanation:
Put a negative next to 2^8 and you'll get your answer.
What is the awnser to pie
A. 3.14195
B. 4.0238
C. 5.3843
D. 6.2322
Answer:
A
Step-by-step explanation:
Suppose a car gas tank holds 21 gallons of gas. On a trip it uses 2/3 of a tank of gas on a trip. Then it uses 1/3 of what is left in the tank. How many gallons of gas are left in the tank? If u can could u show the work?
9514 1404 393
Answer:
2/9 tank
Step-by-step explanation:
After the first trip, 1 -2/3 = 1/3 of the tank remains.
After the second trip, 1 -1/3 = 2/3 of that remains.
After both trips, (1/3 tank)(2/3) = 2/9 tank remains.
Can someone help me with this
C.
Volume of a cylinder is pi times radius squared times height.
Hurry!!!
Review
Bookmark
Wright,
Unit Assessment (MC) / 10 of 13
Gam wants to determine which football team is the most popular at a game between the home team and the visiting
team. Which of the following methods will give him the most accurate results?
A surveying people wearing hats for the visiting team
OB surveying the cheerleaders for the home team
Exhibits
Csurveying people who do not live in the home team's city
OD surveying a group of people standing in line for tickets
Answer:
best person always get best position
Can i get help plz this question rlly hard
Answer:
1890
Step-by-step explanation:
Answer:
I believe your answer is 1512
Step-by-step explanation:
4.2 x 2 = 8.4 this is the area, each inch is equal to 15 feet, there are 180 inches in 15 feet. so 8.4 x 180 = 1512.
A car is traveling at a speed of 75 miles per hour and arrives at its final destination in total of 5.25 hours. What is the distance traveled by the car?
Answer:
86
Step-by-step explanation:
A student runs 7 km in 2 hours to train for sports. What is the student’s average speed?
Answer:
Step-by-step explanation:
For every hour said student would've ran 3.5 km/hr
7/2=3.5 kilometers per hour or 3 1/2 kilometers per hourIn ΔTUV, the measure of ∠V=90°, the measure of ∠U=70°, and UV = 9.6 feet. Find the length of TU to the nearest tenth of a foot.
28.1 feet
explaination
\cos U = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{9.6}{x}
cosU=
hypotenuse
adjacent
=
x
9.6
\cos 70=\frac{9.6}{x}
cos70=
x
9.6
x\cos 70=9.6
xcos70=9.6
Cross multiply.
\frac{x\cos 70}{\cos 70}=\frac{9.6}{\cos 70}
cos70
xcos70
=
cos70
9.6
Divide each side by cos 70.
x=\frac{9.6}{\cos 70}=28.0685\approx 28.1\text{ feet}
x=
cos70
9.6
=28.0685≈28.1 feet
Type into calculator and roundto the nearest tenth of a foot.
Write the equation below in standard form
y = 2/3 x + 5.
this is ur answer i hope u do well good luck:
Answer:
2x-3y=-15
Step-by-step explanation:
Can someone help me with this and explain it?
A water faucet leaked 2 1/6 liters of water every 2/5 of an hour. It leaked at a rate of how many liters per hour?
Enter the value of x.
I need help me this somebody help!
Answer:
M1=136
m4=180-136
=44////
PLZZZZ HELPPPPP BRAINLIEST REWARDD
Answer:
1) Growth
2) y = 3
Explanation:
1) y = a*b^x
y = 3 + 2^x
2 > 1, so it's growth
-4x3 and (x2 + 3x - 4)?
Step-by-step explanation:
Write the ratio as a fraction in simplest from 2ft to 30 in
Step-by-step explanation:
can anyone help? i rlly need help !
please answer the question above, will mark as brainliest answer
Answer:
I think you want to the coordinates of point A
the answer is
(-1,-2)
The least common denominator is the least common multiple of the _______ of the factions fill in the blank
PLEASE ANWSER FOR ME FAST SHOW WORK PLS!!!
Answer:
The answer is A
Step-by-step explanation:
Start at 12 and add 6 every year:
12 + 6 = 18
18 + 6 = 24
24 + 6 = 30
30 + 6 = 36
The perimeter of a square is 66.8 cm. What is the side length of the square?
A) What is the equation that models this situation?
B) Use the equation to find the side length of the square.
Answer:
b
Step-by-step explanation:
Does anyone know how to solve this?
Look at the picture and thanks
Answer:
B
Step-by-step explanation:
I think so I am sorry if I am wrong
Ling baked 72 cookies with 4 scoops of flour. With 5 scoops of flour, how many cookies ca
Ling bake? Assume the relationship is directly proportional.
Answer:
90
Step-by-step explanation:
Divide 72 by 4 you get 18 which is how many Ling baked with one scoop of flour. Then just add 18 to 72 and you get 90