You are working on the newest racing game. Your part is to calculate the speed the car is moving based on acceleration and time. The game determines the acceleration based on how hard the user is pressing the analog trigger button or racing pedal. While the rest of the game is being written, you will write the functions that meet the specifications below.

Function $1$

Function Name

speedDueToAcceleration

Parameters

acceleration : double

time : int

Return Type

double

Description

Takes an acceleration and time value and returns the speed. The time is given in seconds and the acceleration is given in m$/$s$2.$ The formula for calculating speed is s$=$a$$t

s

$=$

a

$$

t

where a is acceleration and t is time.

Function $2$

Function Name: accelerationFromButton

Parameters

buttonForce : double

Return Type

double

Description

Takes a double between $0$ and $10$ representing how hard the user is pressing the acceleration button and converts it to an acceleration in m$/$s$2.$ Use the formula a$=$f$0\mathrm{.}463$

a

$=$

f

$$

$0\mathrm{.}463$

where f is the buttonForce and $0\mathrm{.}463$ is the force to acceleration conversion constant.

Until your functions can be incorporated into the rest of the game, you will need to create a main that prompt for the button force between $0$ and $10$ and the total time in seconds. You will write a program C$++$ that converts the button force to acceleration and then loop starting at time $0$ until the time entered by the user in $3-$second increments. Print a table that shows the speed the vehicle will be traveling at each iteration of the loop$$format the speed and acceleration numbers to $3$ decimal places. Ensure the time entered by the user is the final value shown in the table, even if the total time is not divisible by $3.$ The final value should not be duplicated.

To make sure your functions are compatible with the rest of the game, they will be unit$-$tested.

Input Validation:

You should ensure that the user input does not cause input failure. You should also ensure that the button force is between $0$ and $10$ and that the total time is greater than $0.$

Sample Output:

Enter the button force between $0$ and $10$: $5$

Enter the total acceleration time in seconds: $29$

Acceleration is $2\mathrm{.}315$ m$/$s$^2$

Time in s Speed in m$/$s

$******************************$

$00\mathrm{.}000$

$36\mathrm{.}945$

$613\mathrm{.}890$

$920\mathrm{.}835$

$1227\mathrm{.}780$

$1534\mathrm{.}725$

$1841\mathrm{.}670$

$2148\mathrm{.}615$

$2455\mathrm{.}560$

$2762\mathrm{.}505$

$2967\mathrm{.}135$

Enter the button force between $0$ and $10$: a

You entered something that is not a number. Please Try again.

Enter the button force between $0$ and $10$: $90$

The button force needs to be between $0$ and $10.$

Enter the button force between $0$ and $10$: $-10$

The button force needs to be between $0$ and $10.$

Enter the button force between $0$ and $10$: a

You entered something that is not a number. Please Try again.

Enter the button force between $0$ and $10$: $3$

Enter the total acceleration time in seconds: a

You entered something that is not a number. Please Try again.

Enter the total acceleration time in seconds: $-10$

The total acceleration time must be greater than $0.$

Enter the total acceleration time in seconds: $0$

The total acceleration time must be greater than $0.$

Enter the total acceleration time in seconds: $5$

Acceleration is $1\mathrm{.}389$ m$/$s$^2$

Time in s Speed in m$/$s

$******************************$

$00\mathrm{.}000$

$34\mathrm{.}167$

$56\mathrm{.}945$