All categories

3 years ago

How to prove3 equations of motion graphically

1 answer:

6 0

Consider an object is moving with a uniform acceleration “a” along a straight line. The initial and final velocities of the object at time t = 0 and t = t are u and v respectively. During time t, let s be the total distance travelled by the object.

You might be interested in

To apply Problem-Solving Strategy 12.2 Sound intensity. You are trying to overhear a most interesting conversation, but from you

Ivenika [448]

Answer:

r₂ = 0.316 m

Explanation:

The sound level is expressed in decibels, therefore let's find the intensity for the new location

β = 10 log $\frac{I}{I_o}$

let's write this expression for our case

β₁ = 10 log \frac{I_1}{I_o}

β₂ = 10 log \frac{I_2}{I_o}

β₂ -β₁ = 10 ( $log \frac{I_2}{I_o} - log \frac{I_1}{I_o}$ )

β₂ - β₁ = 10 $log \frac{I_2}{I_1}$

log \frac{I_2}{I_1} = $\frac{60 - 20}{10}$ = 3

$\frac{I_2}{I_1}$ = 10³

I₂ = 10³ I₁

having the relationship between the intensities, we can use the definition of intensity which is the power per unit area

I = P / A

P = I A

the area is of a sphere

A = 4π r²

the power of the sound does not change, so we can write it for the two points

P = I₁ A₁ = I₂ A₂

I₁ r₁² = I₂ r₂²

we substitute the ratio of intensities

I₁ r₁² = (10³ I₁ ) r₂²

r₁² = 10³ r₂²

r₂ = r₁ / √10³

we calculate

r₂ = $\frac{10.0}{\sqrt{10^3} }$

r₂ = 0.316 m

8 0

3 years ago

Two people must have the same speed and velocity if they are walking towards each other, they are walking away from each other,

iVinArrow [24]

Jogging side by side since the speed is equal and the direction is the same i.e same velocity

3 0

3 years ago

A car traveling 34 mi/h accelerates uniformly for 4 s, covering 615 ft in this time. What was its acceleration? Round your answe

Contact [7]

Answer:

51.94 ft/s²

257.63 ft/s

Explanation:

t = Time taken = 4 s

u = Initial velocity = 34 mi/h

v = Final velocity

s = Displacement = 615 ft

a = Acceleration

Converting velocity to ft/s

$34\ mi/h=\frac{34\times 5280}{3600}=49.87\ ft/s$

Equation of motion

$s=ut+\frac{1}{2}at^2\\\Rightarrow a=2\frac{s-ut}{t^2}\\\Rightarrow a=2\left(\frac{615-49.87\times 4}{4^2}\right)\\\Rightarrow a=51.94\ ft/s^2$

Acceleration is 51.94 ft/s²

$v=u+at\\\Rightarrow v=49.87+51.94\times 4\\\Rightarrow v=257.63\ ft/s$

Final velocity at this time is 257.63 ft/s

5 0

3 years ago

A student measures the volume of a gas sample at several different temperatures. The results are tabulated as follows:Temperatur

lapo4ka [179]

Answer:

Check the first and the third choices:

a. The temperature of a gas is directly proportional to its volume

b. The temperature-to-volume ratio of a gas is constant.

Explanation:

Rewrite the table for better understanding:

Temperature of gas (K) Volume of gas (L)

298 4.55

315 4.81

325 4.96

335 ?

Calculate the ratios temperature to volume with 3 significant figures:

298 / 4.55 = 65.5

315 / 4.81 = 65.5

325 / 4.96 = 65.5

Then, those numbers show a constant temperature-to-volume ratio, which may be expressed in a formula as:

Temperature / Volume = constant, which is a directly proportional variation (the volume increases in a constant proportion to the increase of the temperature).

Hence, the correct choices are:

The temperature of a gas is directly proportional to its volume (first statement), and

The emperature-to-volume ratio of a gas is constant (third statement).

5 0

3 years ago

The components of vector A are Ax = +2.2 and Ay = -6.9 , and the components of vector B are given are Bx = -6.1 and By = -2.2. W

Zina [86]

For simplicity, let's call vector B-A vector C Then C is
Cx = (-6.1 - 2.2)
Cy = (-2.2 - (-6.9)) Or,
Cx = -8.3 Cy = 4.7
The magnitude is found with the Pythagorean theorem
||C|| = √(-8.3² + 4.7²) = 9.538

3 0

3 years ago