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
Fiesta28 [93]
3 years ago
14

Two cars A and B, travel in a straight line. The distance of A from the starting point is given as a function of time by x????(?

???) = ???????? + ???????? 2 with ???? = 2.6 m ???? and ???? = 1.20 m/???? 2 . The distance of B from the starting point is x????(????) = ???????? 2 − ???????? 3 with ???? = 2.80 m/???? 2 and ???? = 0.2 m/???? 3 . [a].Which car is ahead just after they leave the starting point? [b].At what time(s) are the cars at the same point? [c]. At what time(s) is the distance from to neither increasing nor decreasing? [d].At what time(s) do A and B have the same acceleration?
Physics
2 answers:
AysviL [449]3 years ago
6 0

Answer:

the Question is incomplete,the complete question is

"Cars A and B travel in a straight line. The distance of A from the starting point is given as a function of time by xA(t)=αt+βt2, with α=2.60m/s and β=1.20m/s2. The distance of B from the starting point is xB(t)=γt2−δt3, with y=2.80m/s2 and δ=0.20m/s3. (a) Which car is ahead just after the two cars leave the starting point? (b) At what time(s) are the cars at the same point? (c) At what time(s) is the distance from A to B neither increasing nor decreasing? (d) At what time(s) do A and B have the same acceleration?"

a.Car A is ahead after leaving the starting point

b.t=0secs,t=2.27secs and t=5.73secs

c.t=1secs and t=4.33secs

d .t=2.67secs

Explanation:

First we need to write out the giving expressions for the distance from the question

For distance A we have

x_{a}(t)=\alpha t +\beta t^{2}\\

and for distance B we have

x_{b}(t)=\gamma t^{2} -\δt^{3}\\.

a.  Note for us to compare the car that will be ahead we need to determine the initial velocity of each car i.e at t=0.

Since the expression for the velocity is not giving, we apply our knowledge of instantaneous motion which involves us differentiating the distance in order to get the velocity.

V=\frac{dx}{dt} \\

and recall  that for y=ax^{n} \\\frac{dy}{dx}=a*nx^{n-1}  \\

for velocity of car  A, we have

v_{a}=\frac{d(\alpha t +\beta t^{2})}{dt}\\v_{a}=\alpha +2\beta t\\

we substitute t=o

v_{a}=\alpha \\\\v_{a}=2.6m/s

for velocity of car  B, we have

v_{b}=\frac{d(\gamma  t^{2} -\delta t^{3})}{dt}\\v_{b}= 2\gamma t  -3\delta t^{2}\\

at t=0

v_{b}=0

in conclusion, since the initial velocity of car An is greater than that of car B, Car A is ahead after leaving the starting point

b. for the time at which the cars are the same point, we need to find the time at which the cars have equal position. this can be done by  equating the position of both cars i.e

x_{a}(t)=x_{b}(t)\\  \alpha t +\beta t^{2}=\gamma t^{2} -\δt^{3}\\

if we carry out simply arithmetic, we arrive at

\delta t^{2}+(\beta -\gamma)t +\alpha =0\\

applying quadratic formula, we determine the value of t to be

t=2.27secs \\t=5.73secs\\

also note that at the starting point before the two cares take-off they are also at the same position i.e at t=0 hence the time which the cars are at the same point are

t=0secs\\t=2.27secs \\t=5.73secs\\

c. the distance will be constant when the two cars move at the same velocity i.e

v_{a}=v_{b} \\

\alpha +2\beta t=2\gamma t -3\delta t^{2}\\

if we rearrange the equation and substitute the value of the constants, we arrive at

0.6t^{2} -3.2t +2.6=0\\

Solving the simple quadratic equation, we arrive at the values of t which are

t=1secs\\t=4.33secs\\

d. To determine the time at which the two cars will have the same acceleration, we need to determine the expression for the acceleration which we can get by differentiating the the velocity for each car

a_{a}(t)=\frac{d(\alpha +2\beta t) }{dt}\\ a_{a}(t)=2\beta \\

and for car B we have the acceleration to be

a_{b}(t)=\frac{d(2\gamma t - 3\delta t^{2})}{dt}\\ a_{b}(t)=2\gamma -6\delta t\\

Hence to have the same acceleration

a_{a}(t)=a_{b}(t)\\2\beta=2\gamma -6\delta t\\

Making t the subject of formula,

t=\frac{\gamma - \beta}{3\delta}\\t=\frac{2.8-1.3}{3*0.2}\\ t=2.67secs\\

Hence the cars will have the same acceleration at t=2.67secs

Norma-Jean [14]3 years ago
3 0

Answer:

a) They are in the same point

b) t = 0 s, t = 2.27 s, t = 5.73 s

c) t = 1 s, t = 4.33 s

d) t = 2.67 s

Explanation:

Given equations are:

x_{a}(t) = at+bt^2

x_{b}(t) = ct^2-dt^3

Constants are:

a = 2.60 m/s, b = 1.20 m/s^2, c= 2.80 m/s^2, d = 0.20 m/s^3

a) "Just after leaving the starting point" means that t = 0. So, if we look the equations, both x_a(t) and x_b(t) depend on t and don't have constant terms.

So both cars A and B are in the same point.

b) Firstly, they are in the same point in x = 0 at t = 0. But for generalized case, we must equalize equations and solve quadratic equation where roots will give us proper t value(s).

at+bt^2 = ct^2-dt^3

2.6t + 1.2t^2 = 2.8t^2 - 0.2t^3\\0.2t^2 - 1.6t + 2.6 = 0\\t^2 - 8t + 13 = 0

t_1 = 4 - \sqrt{3} = 2.27 s, t_1 = 4 + \sqrt{3} = 5.73 s

c) Since the distance isn't changing, the velocities are equal. To find velocities, we need to take the derivatives of both equations with respect to time and equalize them.

v_a(t) = \frac{d}{d(t)}x_a(t) = a + 2bt \\v_b(t) = \frac{d}{d(t)}x_b(t) = 2ct - 3dt^2\\a+2bt = 2ct - 3dt^2\\3dt^2+2(b-c)t+a = 0\\0.6t^2-3.2t+2.6 = 0

t_1 = 1 s, t_2 = 4.33 s

d) For same acceleration, we we need to take the derivatives of velocity equations with respect to time and equalize them.

a_a(t) = \frac{d}{d(t)}v_a(t) = 2b \\a_b(t) = \frac{d}{d(t)}v_b(t) = 2c - 6dt\\2b = 2c - 6dt\\3dt = c - b\\t = (c - b)/3d = (2.8 - 1.2)/(3*0.2) = 2.67 s

You might be interested in
Can you please summarise this, because I can't get the topic
wlad13 [49]
An electric circuit is anything in which electric current flows. Typically it refers to things with wiring like the electronics in your phone, but it can be made of anything that conducts electricity.

Say you have a battery, it basically has a bunch of electrons under a potential (think of gas in a tank under pressure), but the only way for the electrons to move is to move through a conductor, which are molecules with loosely held electrons. If you take a copper wire and touch each end to the two terminals you’ve completed an electric circuit because the electrons can now flow. But you can also put things partway through the wire like a lightbulb, which when the electrons run through it generates light.
4 0
3 years ago
Which statement describes why scientific notation is useful? It makes very small numbers into whole numbers. It converts fractio
disa [49]

It makes calculations with very large and small numbers easier.

Scientific notation is a system used in order to It makes calculations with very large and small numbers easier. It is useful as it allows very large number that would take a lot of space to write otherwise, and it allows them to be calculated easier. 10^{23} for example is a incredible large number, but written in this form is immediately understandable and useful for calculation.

3 0
3 years ago
Read 2 more answers
Measurements of acceleration are given in units of ?
Lady_Fox [76]
Meters per second squared: \frac{m}{s^{2}}

If you think about it, acceleration is about how fast speed changes. Speed is measured in meters per second: \frac{m}{s}

So if you take that and just measure it over time, you get meters per second squared.
3 0
3 years ago
Read 2 more answers
a spherical mirror is cut in half horizontally will an image be formed by the bottom half of the mirror how
monitta

Answer:

Explanation:

the spherical mirror can form an image even if it is cut in half horizontally , but the image formed may be blurred.

pls mark as brainliest if you find it helpful

7 0
2 years ago
If we put a convex lens made by crown glass <br>in Carbondia sulphide what will happen?​
7nadin3 [17]

Answer:

I don't knowI think it will break

4 0
2 years ago
Other questions:
  • Which statement about the horizontal distance covered by a projectile launched at an angle less than 90° is true?
    13·1 answer
  • What are three benefits of being assertive and what are three tips to help you develop an assertive style of communication? (Sit
    7·1 answer
  • A 70-kg pole vaulter running at 11 m/s vaults over the bar. Her speed when she is above the bar is 1.3 m/s. Neglect air resistan
    5·1 answer
  • Newton's law of universal gravitation can be applied to
    5·2 answers
  • Which term refers to the structure that forms the surface of a cell separating its contents from the outside world
    5·2 answers
  • Plz help with atomic question giving brianly.
    8·2 answers
  • When the ball on the table starts moving when the table is tilted
    14·1 answer
  • Should young children be treated as “little adults”? Based on what you have learned about development, do you think that is reas
    12·2 answers
  • You have a length of tubing that is closed at one end. You cut the tubing into two pieces of unequal length, giving you a tube o
    6·1 answer
  • I need it in the next hour or so!
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!