1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
worty [1.4K]
2 years ago
14

8. A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right. The equation f

or the turtle's position as a function of time is x(t) = 5.0 cm + (4.00 cm/s) - (0.625 cm/s2)t2. (a) Find the turtle's initial velocity, initial position, and initial acceleration. (b) At what time is the velocity of the turtle zero? (c) How long after starting does it take the turtle to return to its starting point? (d) At what times t is the turtle a distance of 30.00 cm from its starting point? What is the velocity at each of these times?​
Physics
1 answer:
pychu [463]2 years ago
7 0

(a) The turtle's initial velocity is 4 m/s, initial position of the turtle is 5 cm, and initial acceleration is -1.25 m/s².

(b) The time when the velocity of the turtle is zero is 3.2 s.

(c) The time taken for the turtle to return to its starting point is 6.4 s.

(d) The time taken for the turtle to travel 30 cm is 0.08 s.

<h3>Initial velocity of the turtle</h3>

The initial velocity of the turtle is calculated as follows;

v = \frac{dx}{dt} \\\\x = 5 + 4t -0.625t^2\\\\v(t) = 4 - 1.25t\\\\v(0) = 4-0\\\\v(0) = 4 \ m/s

<h3>Initial acceleration of the turtle</h3>

The initial acceleration of the turtle is calculated as follows;

a = \frac{dv}{dt} \\\\v(t) = 4 - 1.25t\\\\a = -1.25\ m/s^2

<h3>Initial position of the turtle</h3>

x(t) = 5 + 4t - 0.625t²

x(0) = 5 cm

<h3>Time when the velocity becomes zero</h3>

v(t) = 4 - 1.25t

0 = 4 - 1.25t

1.25t = 4

t = 4/1.25

t = 3.2 s

<h3>Time taken to return to starting point</h3>

The total distance traveled is calculated as follows

v² = u² + 2ad

0 = (4)² + 2(-1.25)d

0 = 16 - 2.5d

2.5d = 16

d = 16/2.5

d = 6.4 m

Time to travel the given distance;

d = ut + ¹/₂at²

6.4 = (4)t + ¹/₂(-1.25)t²

6.4 = 4t - 0.625t²

0.625t² - 4t + 6.4 = 0

solve the quadratic equation using formula method;

t = 3.2 s

The time travel the distance two times, = 2 x 3.2 s = 6.4 s

<h3>Time taken for the turtle to travel 30 cm</h3>

d = ut + ¹/₂at²

0.3 = (4)t + ¹/₂(-1.25)t²

0.3 = 4t - 0.625t²

0.625t² - 4t + 0.3 = 0

solve the quadratic equation using formula method;

t = 0.08 s

Learn more about velocity here: brainly.com/question/6504879

You might be interested in
A student uses the right-hand rule as shown.
m_a_m_a [10]

Answer: O:right

Explanation: In this case you place your finger on the current, and your fingers should curl showing the way, you must use your right hand in this case, otherwise that would mean the fingers on your left would bend way back, and snap off, (Not really lol,  just saying)

5 0
2 years ago
You exert a force of 75 newtons on a rock. You push and you push, but you can’t budge it. You are exhausted! How much work did y
dalvyx [7]

Answer:   Work W = 0

Explanation: Work W = F·s. Because rock does not move, s = 0 and

work done is zero.

4 0
2 years ago
You find a micrometer (a tool used to
MakcuM [25]

Explanation:

A micrometer is a measuring device or an instrument which is used to measure very minute measurements very accurately and precisely. It is mathematical tool used to provide accurate measurement for any mechanical components.

Now, if the micrometer that I have found is badly bent, it would provide faulty or wrong measurements both in terms of  precision and accuracy when compared to a high quality meter stick.

3 0
3 years ago
In the rectangle to the left, if
Margarita [4]

perimeter of a rectangle = 2(L+B)

90=2(L+B)

90/2=L+B

45=L+B

7 0
3 years ago
Which kind of energy transformation occurs during skydiving? A) mechanical to gravitational B) gravitational to kinetic C) kinet
Aleks [24]

B) gravitational to kinetic

Explanation:

The skydiver, when he is located at a certain height h above the ground, possesses gravitational potential energy, equal to:

U=mgh

where m is the mass of the skydiver, g is the gravitational acceleration and h is the height above the ground. As he falls, its height h decreases, while his speed v increases, so part of the gravitational potential energy is converted into kinetic energy, which is given by

K=\frac{1}{2}mv^2

so, we see that as v increases, the kinetic energy increases. Therefore the correct answer is

B) gravitational to kinetic

7 0
3 years ago
Read 2 more answers
Other questions:
  • If the cold temperature reservoir of a Carnot engine is held at a constant 306 K, what temperature should the hot reservoir be k
    13·1 answer
  • In a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so
    15·1 answer
  • Tell me about your favorite science experiment. Give me a detailed account of the experiment and what you like about it.​
    6·1 answer
  • Which is a charcharacteristic of all ions?
    5·1 answer
  • Five hundred million years ago, basaltic lava flowed in an area now known as Monticello, the historic home of Thomas Jefferson.
    14·1 answer
  • What’s the meaning of Obesity
    8·1 answer
  • Digestion and breathing are _____.
    5·1 answer
  • The two pictures below show an area where a major geologic process has occurred. Explain which process caused the formation, giv
    11·1 answer
  • A body is dropped from the roof of a 20 m high building by how much:
    11·1 answer
  • The nucleus is found in the center of an atom options: True False
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!