The law of conservation of energy applies:

A ride-sharing car moving along a straight section of road starts from rest, accelerating at 2.00 m/s2 until it reaches a speed

liq [111]

Answer:

A) total time = 55.5 seconds

B) average velocity = 25.27 m/s

Explanation:

It starts from rest, so initial velocity, u = 0 m/s

We are given;

acceleration; a = 2 m/s²

Final velocity; v = 31 m/s

From Newton's first law of motion,

v = u + at

So, 31 = 0 + 2t

t = 31/2

t = 15.5 sec

We are told that, after this time of 15.5 sec, the car travels 35 sec at a constant speed and after that it takes 5 sec additional time to stop. Thus;

(a) Total time in which car is in motion = 15.5 + 35 +5 = 55.5 seconds

b)Total distance traveled during first 15.5 sec would be gotten from Newton's second equation of motion which is;

S = ut + ½at²

S1 = 0 + ½(2 * 15.5²)

S1 = 240.25 m

Distance traveled in 35 sec with with velocity of 31 m/sec is;

S2 = velocity x time

S2 = 35 × 31 = 1085 m

Now, for the final stage, final velocity (v) will now be 0 since the car comes to rest while initial velocity(u) will be 31 m/s.

From the first equation of motion,

a = (v - u)/t

a = (0 - 31)/5

a = -6.2 m/s²

So, distance travelled is;

S3 = ut + ½at²

S3 = (31 × 5) + ½(-6.2 × 5²)

S3 = 155 - 77.5

S3 = 77.5 m

So overall total distance = S1 + S2 + S3

Overall total distance = 240.25 + 1085 + 77.5 = 1402.75 m

Average velocity = total distance/total time

Average velocity = 1402.75/55.5 = 25.27 m/s

6 0

3 years ago

A spaceship moves radially away from Earth with acceleration 29.4 m/s 2 (about 3g). How much time does it take for sodium street

Gemiola [76]

Answer:

doppler shift's formula for source and receiver moving away from each other:

λ'=λ°√(1+β/1-β)

Explanation:

acceleration of spaceship=α=29.4m/s²

wavelength of sodium lamp=λ°=589nm

as the spaceship is moving away from earth so wavelength of earth should increase w.r.t increasing speed until it vanishes at λ'=700nm

using doppler shift's formula:

λ'=λ°√(1+β/1-β)

putting the values:

700nm=589nm√(1+β/1-β)

after simplifying:

β=0.17

by this we can say that speed at that time is: v=0.17c

to calculate velocity at an acceleration of a=29.4m/s²

we suppose that spaceship started from rest so,

v=v₀+at

where v₀=0

so v=at

as we want to calculate t so:-

t=v/a v=0.17c ,c=3x10⁸ ,a=29.4m/s²

putting values:

=0.17(3x10⁸m/s)/29.4m/s²

t=1.73x10⁶

7 0

3 years ago

Use the drop-down menus to complete each sentence about the layers of the atmosphere. If the did not exist, Earth might be destr

ozzi

Answer:

If the mesosphere did not exist, Earth might be destroyed by chunks of rock from space.

The stratosphere is located 12 to 50 kilometers from Earth's surface.

Both the trophosphere and mesosphere get colder as altitude increases.

The ozone in the stratosphere protects people from ultraviolet (UV) radiation.

The thermosphere has the highest temperature of any layer in Earth's atmosphere.

Explanation:

Different layers of the atmosphere are;

Troposphere

It is the lowest layer of atmosphere that begins at ground level and extends upward to about 10 km. In this layer, all organisms live, weather occurs and most clouds appear. As altitude increases, the temperature decreases i.e., the layer gets colder.

Stratosphere

This layer is located at the top of the troposphere and extends up to about 50 km from Earth's surface. The ozone layer present in this layer absorbs high-energy ultraviolet (UV) light from the Sun. Here, the temperature rises with altitude. The passenger jets are usually fly in this layer.

Mesosphere

Above the stratosphere, the mesosphere extends upward to about 85 km from Earth's surface. The chunks of rock from space such as meteors burn upon entering the mesosphere and protect the Earth. In this layer, the temperature gets colder as altitude increases and so the coldest temperatures (about -90° C) in Earth's atmosphere are found at the top of this layer.

Thermosphere

This layer is located above the mesosphere and the air here is really very thin. The thermosphere absorbs high-energy X-rays and UV radiation from the Sun and as a result, its temperature increases to hundreds or thousands of degrees i.e., 1,500° C or higher. This layer extends up to 500 to 1,000 km from the ground. Many satellites orbit Earth within this layer.

Ionosphere

The ionosphere is actually an extension of the thermosphere and so it is not a distinct layer like the others. It is filled with charged particles produced from the ionization of molecules by high temperatures in the thermosphere caused by the high-energy radiation from the Sun. The phenomenon called auroras (Northern Lights and Southern Lights) occurs in this layer. The different regions of the ionosphere reflecting the radio waves back to Earth and make the long-distance radio communication possible.

4 0

3 years ago

Read 2 more answers

A 270,000 kg rocket in gravity -free space expels 270 kg of fuel by exerting a force of 360 N on it. Find the magnitude of the a

Brut [27]

F = m a
360 = 270 x a
1.3 = a

4 0

3 years ago

A BMX bicycle rider takes off from a ramp at a point 2.4 m above the ground. The ramp is angled at 40 degrees from the horizonta

adoni [48]

Answer:

The BMX lands 5.4 m from the end of the ramp.

Explanation:

Hi there!

The position of the BMX is given by the position vector "r":

r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)

Where:

r = position vector at time t

x0 = initial horizontal position

v0 = initial velocity

α = jumping angle

y0 = initial vertical position

g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive)

Please, see the attached graphic for a better understanding of the situation. At final time, when the bicycle reaches the ground, the vector position will be "r final" (see figure). The y-component of the vector "r final" is - 2.4 m (placing the origin of the frame of reference at the jumping point). With that information, we can use the equation of the y-component of the vector "r" (see above) to calculate the time of flight. With that time, we can then obtain the x-component (rx in the figure) of the vector "r final". Then:

y = y0 + v0 · t · sin α + 1/2 · g · t²

-2.4 m = 0 m + 5.9 m/s · t · sin 40° - 1/2 · 9.8 m/s² · t²

0 = -4.9 m/s² · t² + 5.9 m/s · t · sin 40° + 2.4 m

Solving the quadratic equation:

t = 1.2 s

Now, we can calculate the x-component of the vector "r final" that is the horizontal distance traveled by the bicycle:

x = x0 + v0 · t · cos α

x = 0 m + 5.9 m/s · 1.2 s · cos 40°

x = 5.4 m

The BMX lands 5.4 m from the end of the ramp.

Have a nice day!

8 0

3 years ago