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
MrRissso [65]
3 years ago
6

A train starts at rest in a station and accelerates at a constant 0.987 m/s2 for 182 seconds. Then the train decelerates at a co

nstant 0.321 m/s2 until it comes to a stop at the next station. Find the distance between the stations, in km.
Physics
1 answer:
algol [13]3 years ago
8 0

Answer:

\displaystyle X_T=66.6\ km

Explanation:

<u>Accelerated Motion </u>

When a body changes its speed at a constant rate, i.e. same changes take same times, then it has a constant acceleration. The acceleration can be positive or negative. In the first case, the speed increases, and in the second time, the speed lowers until it eventually stops. The equation for the speed vf at any time t is given by

\displaystyle V_f=V_o+a\ t

where a is the acceleration, and vo is the initial speed .

The train has two different types of motion. It first starts from rest and has a constant acceleration of 0.987 m/s^2 for 182 seconds. Then it brakes with a constant acceleration of -0.321 m/s^2 until it comes to a stop. We need to find the total distance traveled.

The equation for the distance is

\displaystyle X=V_o\ t+\frac{a\ t^2}{2}

Our data is

\displaystyle V_o=0,a=0.987m/s^2,\ t=182\ sec

Let's compute the first distance X1

\displaystyle X_1=0+\frac{0.987\times 182^2}{2}

\displaystyle X_1=16,346.7\ m

Now, we find the speed at the end of the first period of time

\displaystyle V_{f1}=0+0.987\times 182

\displaystyle V_{f1}=179.6\ m/s

That is the speed the train is at the moment it starts to brake. We need to compute the time needed to stop the train, that is, to make vf=0

\displaystyle V_o=179.6,a=-0.321\ m/s^2\ ,V_f=0

\displaystyle t=\frac{v_f-v_o}{a}=\frac{0-179.6}{-0.321}

\displaystyle t=559.5\ sec

Computing the second distance

\displaystyle X_2=179.6\times559.5\ \frac{-0.321\times 559.5^2}{2}

\displaystyle X_2=50,243.2\ m

The total distance is

\displaystyle X_t=x_1+x_2=16,346.7+50,243.2

\displaystyle X_t=66,589.9\ m

\displaystyle \boxed{X_T=66.6\ km}

You might be interested in
What effect does Earth’s spherical shape have on the amount of sunlight that reaches the equator?
Natasha_Volkova [10]
Because the Earth<span> is a sphere, the surface gets much more intense </span>sunlight<span>, hence heat, at </span>the equator<span>than at the poles.</span>
6 0
3 years ago
Read 2 more answers
An ore car of mass 39000 kg starts from rest and rolls downhill on tracks from a mine. At the end of the tracks, 25 m lower vert
Musya8 [376]

Answer:

x = 5.79 m

Explanation:

given,

mass of the car = 39000 Kg

spring constant = 5.7 x 10⁵ N/m

acceleration due to gravity = 9.8 m/s²

height of the track = 25 m

length of spring compressed = ?

using conservation of energy

potential energy is converted into spring energy

m g h = \dfrac{1}{2}kx^2

x =\sqrt{\dfrac{2 m g h}{k}}

x =\sqrt{\dfrac{2\times 39000 \times 9.8 \times 25}{5.7 \times 10^{5}}}

x =\sqrt{33.5263}

x = 5.79 m

the spring is compressed to x = 5.79 m to stop the car.

3 0
3 years ago
Is it possible that a speed of 254 and a speed of 100 could be the same speed?
EastWind [94]
Not if both speeds are in the same units.

However, if the 254 is 'centimeters per time' and the 100 is 'inches per time',
then the speeds are equal.
4 0
3 years ago
Describe the difference between a soil horizon and a soil profile
mario62 [17]

Soil profile includes all the sections/ horizons of the vertical soil depth from top to bottom including the transitions from one horizon to another. A soil horizon is a distinct layer/section of soil with more or less the same texture. Therefore, a soil profile is made of soil horizons.  

5 0
3 years ago
Read 2 more answers
10. Inertia causes your books on the car seat to continue moving forward even after you brake. TrueFalse 11. Tires with little o
Charra [1.4K]

10. True

11. True

12. True

13. False

14. False

Hope this helps!!

3 0
3 years ago
Other questions:
  • A cable with mass 0.5 kilograms per meter (kg/m) is used to lift 150 kg of coal up a mine shaft 50 meters deep. Set up the integ
    12·1 answer
  • A tow truck pulls a 2,000-kilogram car with a net force of
    12·1 answer
  • A planet has two
    7·1 answer
  • How is the kelvin scale different from the Celsius scale?
    6·1 answer
  • How many water (in kg) can raise its temperature from 23°C to 100°C by adding 21500 Joules of energy?
    12·1 answer
  • First, you will investigate purely vertical motion. The kinematics equation for vertical motion (ignoring air resistance) is giv
    5·1 answer
  • A tuning fork produced four beats per second with a second, 270-Hz tuning fork. What are the two possible frequencies of the fir
    11·1 answer
  • Question 1
    14·1 answer
  • What is the average income of an osteologist? (Anatomy)
    6·1 answer
  • You're driving a bumper car at a circus at
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!