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eimsori [14]
3 years ago
5

A ball at rest rolls across a frictionless floor at 12.0 m/s/s. How far will it travel in

Physics
1 answer:
professor190 [17]3 years ago
3 0

Answer:

The distance, d travelled by the ball is 768 metres.

Explanation:

In physics, acceleration can be defined as the rate of change of the velocity of an object with respect to time.

This simply means that, acceleration is given by the subtraction of final speed from the initial speed all over time.

Hence, if we subtract the final speed from the initial speed and divide that by the time, we can calculate an object’s acceleration.

Mathematically, acceleration is given by the equation;

Acceleration (a) = \frac{initial \; speed  -  final \; speed}{time}

a = \frac{v  -  u}{t}

Where,

a is acceleration measured in ms^{-2}

v and u is initial and final speed respectively, measured in ms^{-1}

t is time measured in seconds.

Given the following data;

Acceleration = 12.0m/s²

Time, t = 8secs

Velocity =?

First, we would calculate its velocity;

a = \frac{v  -  u}{t}

Since the ball rolls at rest, initial velocity is zero (0).

V = a * t

V = 12 * 8

Velocity = 96ms^{-1}

We can now solve for the distance;

Velocity = \frac{distance}{time}

Therefore,

Distance = velocity * time

Distance = 96 * 8

Distance = 768m.

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A 250 g air-track glider is attached to a spring with springconstant 4.0 N/m. Th damping constant due to air resistance is0.015
vaieri [72.5K]

Answer:

33.33 seconds

Explanation:

N=\dfrac{1}{e}N_0

N_0 = Initial length pulled = 20 cm

b = Damping constant = 0.015 kg/s

k = Spring constant = 4 N/m

m = Mass of glider = 250 g

Time period is given by

T=2\pi\sqrt{\dfrac{m}{k}}\\\Rightarrow T=2\pi\sqrt{\dfrac{0.25}{4}}\\\Rightarrow T=1.57079632679\ s

Using exponential decay formula

N=N_0e^{\dfrac{-bt}{m}}

Final amplitude = Initial times decay

\dfrac{1}{e}0.2=0.2e^{\dfrac{-0.015t}{2\times 0.25}}\\\Rightarrow 0.2=0.2e^{\frac{-0.015t}{2\cdot \:0.25}+1}\\\Rightarrow e^{\frac{-0.015t}{2\cdot \:0.25}+1}=1\\\Rightarrow \ln \left(e^{\frac{-0.015t}{2\cdot \:0.25}+1}\right)=\ln \left(1\right)\\\Rightarrow \left(\frac{-0.015t}{2\cdot \:0.25}+1\right)\ln \left(e\right)=\ln \left(1\right)\\\Rightarrow \frac{-0.015t}{2\cdot \:0.25}+1=\ln \left(1\right)\\\Rightarrow -\frac{0.015t}{0.5}=-1\\\Rightarrow -0.000225t=-0.0075\\\Rightarrow t=33.33\ s

The time taken is 33.33 seconds

7 0
3 years ago
Acrostic poem for transformation
Julli [10]

An acrostic poem for transformation simply refers to those simple poems conveying transformation messages in which the first letter of each line forms a word or phrase vertically.

<h3>What is poem?</h3><h3 />

A poem can be defined as a a piece of writing in which the expression of feelings and ideas is given intensity by particular attention to diction.

So therefore, an acrostic poem for transformation simply refers to those simple poems conveying transformation messages in which the first letter of each line forms a word or phrase vertically.

Complete question:

What do you understand by acrostic poem for transformation?

Learn more about poem:

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5 0
2 years ago
A garden hose with a diameter of 0.64 in has water flowing in it with a speed of 0.46 m/s and a pressure of 1.9 atmospheres. At
STALIN [3.7K]

Answer:

(a).The speed of the water in the nozzle is 3.014 m/s.

(b). The pressure in the nozzle is 1.86 atm.

Explanation:

Given that,

Nozzle diameter = 0.25 in = 0.00635 m

Hose pipe diameter = 0.64 in = 0.016256 m

Pressure = 1.9 atm =192518 Pa

(a). We need to calculate the speed of the water in the nozzle

Flow Speed at the inlet pipe will be given by using Continuity Equation

Q_{1}=Q_{2}

v_{1}A_{1}=v_{2}A_{2}

v_{1}=v_{2}\times(\dfrac{A_{2}}{A_{1}})

Where, A = area of pipe

A=\pi\times \dfrac{d^2}{4}

v_{1}=v_{2}\times(\dfrac{d_{2}^2}{d_{1}^2})

Put the value into the formula

v_{1}=0.46\times\dfrac{(0.016256)^2}{(0.00635)^2}

v_{1}=3.014\ m/s

The speed of the water in the nozzle is 3.014 m/s.

(b). We need to calculate the pressure in the nozzle

Using Bernoulli's Theorem,

P_{1}+\dfrac{1}{2}\rho\times v_{1}^2+\rho gh_{1}=P_{2}+\dfrac{1}{2}\rho\times v_{2}^2+\rho gh_{2}

Where, h_{1}=h_{2}

P_{1}+\dfrac{1}{2}\rho\times v_{1}^2=P_{2}+\dfrac{1}{2}\rho\times v_{2}^2

P_{1}=P_{2}+\dfrac{1}{2}\rho(v_{2}^2-v_{1}^2)

Put the value into the formula

P_{1}=192518 +\dfrac{1}{2}\times1000\times((0.46)^2-(3.014)^2)

P_{1}=188081.702\ Pa

P=1.86\ atm

Hence, (a).The speed of the water in the nozzle is 3.014 m/s.

(b). The pressure in the nozzle is 1.86 atm.

7 0
3 years ago
An object of mass 20kg is released from a height of 10 meters above the ground level. The kinetic energy of the the object just
Yuri [45]

Answer:

The answer is the object weighs 5 so 3-5 is 2

Explanation:

I took this test

7 0
2 years ago
A small sphere is at rest at the top of a frictionless semicylindrical surface. The sphere is given a slight nudge to the right
V125BC [204]

Answer:

vi = 4.77 ft/s

Explanation:

Given:

- The radius of the surface R = 1.45 ft

- The Angle at which the the sphere leaves

- Initial velocity vi

- Final velocity vf

Find:

Determine the sphere's initial speed.

Solution:

- Newton's second law of motion in centripetal direction is given as:

                         m*g*cos(θ) - N = m*v^2 / R

Where, m: mass of sphere

             g: Gravitational Acceleration

             θ: Angle with the vertical

             N: Normal contact force.

- The sphere leaves surface at θ = 34°. The Normal contact is N = 0. Then we have:

                         m*g*cos(θ) - 0 = m*vf^2 / R

                         g*cos(θ) = vf^2 / R    

                         vf^2 = R*g*cos(θ)

                         vf^2 = 1.45*32.2*cos(34)

                        vf^2 = 38.708 ft/s

- Using conservation of energy for initial release point and point where sphere leaves cylinder:

                          ΔK.E = ΔP.E

                          0.5*m* ( vf^2 - vi^2 ) = m*g*(R - R*cos(θ))

                          ( vf^2 - vi^2 ) = 2*g*R*( 1 - cos(θ))

                          vi^2 =  vf^2 - 2*g*R*( 1 - cos(θ))

                          vi^2 = 38.708 - 2*32.2*1.45*(1-cos(34))

                          vi^2 = 22.744

                           vi = 4.77 ft/s

4 0
3 years ago
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