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
Bezzdna [24]
3 years ago
13

A student is running at her top speed of 5.4 m/s to catch a bus, which is stopped at the bus stop. When the student is still a d

istance 38.5 m from the bus, it starts to pull away, moving with a constant acceleration of 0.171 m/s2.
a) For how much time and what distance does the student have to run at 5.4m/s before she overtakes the bus?
b) When she reaches the bus how fast is the bus traveling
c) Sketch an x-t graph for both the student and the bus. Take x=0 at the initial position of the student
d) the equations you used in part a to find the time have a second solution, corresponding to a later time for which the student and bus are again at the same place if they continue thier specified motion. Explain the significance of this second solution. How fast is the bus traveling at this point
e) If the students top speed is 3.5 m/s will she catch the bus?
f) is the minumun speed the student must have to just catch up with the bus? For what time and distance must she run in that case

Physics
1 answer:
olya-2409 [2.1K]3 years ago
4 0

Answer:

a) t=8.19s; x=44.2m

b) v=1.401 m/s

c) see attachment

d) The second solution is a later time at which the bus catches the student. v=9.40 m/s

e) No, she won't.

f) v=3.63m/s;t=21.2; x=77m

Explanation:

a) The motion of both the bus and the student can be explained by the equation x= v_{0} +\frac{1}{2}at^{2}. Since the student is not accelerating, but rather maintaining a constant speed; the particular equation that describes the motion of the student is: x_{student} = 5.4 \frac{m}{s} * t. Meanwhile, since the bus starts its motion at an initial velocity of zero, the equation that describes its motion is: x_{bus} =\frac{1}{2} * 0.171 \frac{m}{s^{2} } * t^{2}. The motion of the student relative to that of the bus can be described by the equation: x_{s} =x_{bus} +38.5m. By replacing terms in the last equation we end up with the following quadratic equation: (0.0855 \frac{m}{s^{2} } * t^{2} )-(5.4\frac{m}{s} *t)+38.5m =0. Solving the quadratic equation will yield two solutions; t1=8.19s and t2=55.0s. By plugging in t1 onto the equation that describes the motion of the student we will find the distance runned by her, x=44.2m.

b) The velocity of the bus can be modeled by the equation v^{2} = v_{0} ^{2} +2ax. Since the initial velocity of the bus is zero, the first term of the equation cancels. Next, we solve for v and plug in the acceleration of 0.171 m/s2 and the distance 5.74m (traveled by the bus, note: this is equal to the 44.2m travelled by the student minus the 38.5m that separated the student from the bus at the beginning of the problem).

c) The equations that make up the x-t graph are: x = 5.4 \frac{m}{s} * t and  x =\frac{1}{2} * 0.171 \frac{m}{s^{2} } * t^{2} + 38.5; as described in part a.

d) The first solution states that the student would have to run 44.2 m in 8.19 s in order to catch the bus. But, at that point, the student has a greater speed than that of the bus. So if both were to keep he same specified motion, the student would run past the bus until it reaches a velocity greater than that of the student. At which point, the bus will start to narrow the distance with the student until it finally catches up with the student 55 seconds after both started their respective motion.

e) No, because the quadratic equation (0.0855 \frac{m}{s^{2} } * t^{2} )-(3.5\frac{m}{s} *t)+38.5m =0 has no solution. This means that the two curves that describe the distance vs time graph for both student and bus do not intersect.

f) This answer is reached by finding b of the quadratic equation. The minimum that b can be in order to find a real answer to the quadratic equation is found by solving b^{2} -4ac=0. If we take a = 0.0855 and c = 38.5, then we find that the minimum speed that the student has to run at is 3.63 m/s. If we then solve the quadratic equation (0.0855 \frac{m}{s^{2} } * t^{2} )-(3.63\frac{m}{s} *t)+38.5m =0,we will find that the time the student will run is 21.2 seconds. By pluging in that time in the equation that describes her motion: x_{student} = 3.63 \frac{m}{s} * t we find that she has to run 77 meters in order to catch the bus.

You might be interested in
_____ replacement involves one element replacing another element in a compound.
Scorpion4ik [409]

Answer:

Single replacement

Explanation:

A single replacement reaction is a reaction in which the less reactive elements are replaced by the more reactive element in a compound. This is so because the more reactive element are higher in the electrochemical series element than the less reactive elements

3 0
3 years ago
Technician A says that one heater hose should be hot and the other hose cool if the heater is functioning okay. Technician B say
Alika [10]

Answer:

The correct answer to the question is

B) Technician B only

Explanation:

A heater hose is a relatively inexpensive rubber hose used to transmit engine coolant though the engine to the radiator that supplies the heat required in the cabin. They normally extend from the engine to the dash board.

The heater hoses should be hot. If the hoses are cold, it is an indication of a blocked flow from either the heater control valves is blocked   or the radiator becoming clocked with debris.

4 0
3 years ago
A lunar eclipse can only happen during a(1) new moon.(2) solstice.(3) first quarter moon.(4) full moon.(5) perihelion passage of
Ray Of Light [21]

Answer:

(4) full moon.

Explanation:

Lunar eclipse can only occur on a full moon night when the sun the earth and the moon are very much in a straight line.

During this period the the light of the sun that incidents on the moon is blocked by the earth and so we have the phases of the moon due to the relative motion of the three bodies which partially enables the light of the sun to reach the moon.

The moon appears orange-red during this time because the light that reaches the moon is after the refraction through the earth's atmosphere from which the other wavelengths have been absorbed by the earth's atmosphere.

Lunar eclipse can only occur at night and hence it can only be observed from about half of the earth.

7 0
3 years ago
2.486 L is equal to:
swat32
Is equal to 2486 milliliters
8 0
3 years ago
Read 2 more answers
Advantages of outsourcing project work may likely include all of the following EXCEPT:
yaroslaw [1]

Answer:

e. Reduced conflict.

Explanation:

Outsourcing is a tool that allows you to hire a provider outside the company for the execution of secondary activities, such as cleaning or mail, or covering other areas of the company, such as financial or accounting systems or the human resources area

- Advantages of Outsourcing

- Cost reduction

- Focus on the main activity

- Transformation of fixed costs into variables

- Reduce risk

- Improve quality

- Productivity increase

- Improve innovation processes

- Greater flexibility

- Access to the latest technologies

- Increase in competitiveness

3 0
3 years ago
Other questions:
  • 2. A/An _______ is composed of two or more types of matter that can be present in varying amounts.
    12·2 answers
  • How can a comet become the source of meteoroids and meteors?
    8·2 answers
  • Two objects of different mass rest on Earth. Which one experiences the greater acceleration due to gravity ?
    5·1 answer
  • A feeding buffer protects ______ path from delays in ______ ____.
    11·1 answer
  • Which physical property refers to the temperature at which a substance in a solid-state transforms to a liquid state?
    9·2 answers
  • Doing work alawyas means blank energy​
    11·1 answer
  • Thor deja caer su martillo de la torre Torre Stark que tiene 95 pisos, si al llegar el Mjolnir al piso han transcurrido 9.5 segu
    14·1 answer
  • HELPPP BESTIESSS An astronomer is studying two stars that have about the same size and brightness. From the Earth, one of the st
    8·2 answers
  • You have learned how to create an effective study space in this learning path.
    10·1 answer
  • A van of mass 5,000kg travelling at a velocity of 10 m/s collides with a stationary car. The vehicles move together after the im
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!