A wheel which is initially at rest starts to turn with a constant angular acceleration. After 4 seconds it has made 4 complete revolutions. 1)How many revolutions has it made after 8 seconds

To simplify question, the motion of a point on the wheel along a circular

path is assumed to be at a constant angular rate.

The number of revolution made by the wheel after 8 seconds is = 16

revolutions.

Reasons:

The given parameters are;

The motion of the wheel = Constant angular acceleration.

Number of revolutions made after four seconds = 4

Required:

The number of revolutions made after 8 seconds.

Solution:

The formula for finding the angle turned in an angular motion is similar to

the formula for finding the distance moved in linear motion.

For linear motion, we have;

s = u·t = (1/2)·a·t²

For an angular motion, we have;

θ = ω₀·t + (1/2)·α·t²

Where;

ω₀ = The given initial angular velocity = 0

α = angular acceleration

Therefore, for 4 revolutions, we have;

4×π×2 = 0 × 4 + (1/2) × α × 4² = 8·α

Therefore;

α = π

After 8 seconds, we have;

θ =  0 × 8 + (1/2) × π × 8² = 32·π

The angle turned after 8 seconds = 32·π

1 revolution = 2·π

Therefore;

The number of revolution made by the wheel after 8 seconds is = 16 revolutions.

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16

Step-by-step explanation:

We are given that

Initial velocity,=0

Time=4 s

Number of revolutions in 4 s=4 rev=

Because 1  re= rad

We have to find the number of revolutions made by wheel after 8 s.

Using the formula

Again, t=8

Number of rev=

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

11

step-by-step explanation:

32.50-7.50=25

225/25=11