Formula Practice

Each of these gives you a formula and asks for a program. The work is the translation: naming the symbols, ordering the steps, and deciding what the user has to type. Answer on paper first — the whole difficulty is in the plan, not the typing.

1. Distance travelled

$d=v\times t$

Ask for a speed in kilometres per hour and a time in hours, print the distance to one decimal place.

Answer 1

When it asks, type a speed and then a time.

speed = float(input("Speed, in km/h: "))
time_taken = float(input("Time, in hours: "))
 
distance = speed * time_taken
 
print(f"Distance travelled: {distance:.1f} km")

The units are in the prompts on purpose. A program that accepts a speed in metres per second and calls the answer kilometres is arithmetically perfect and completely wrong.

2. Area of a circle

$A=\pi r^2$

Ask for a radius, print the area to two decimals. Use math.pi, not 3.14.

Answer 2

When it asks, type a radius.

import math
 
radius = float(input("Radius, in cm: "))
 
area = math.pi * radius ** 2
 
print(f"Area: {area:.2f} square cm")

radius ** 2 is squaring; radius * 2 is a different program that will look fine and be wrong for every input except 2.

3. Celsius to Fahrenheit

$F=\frac{9}{5}C+32$

Answer 3

When it asks, type a temperature.

celsius = float(input("Temperature, in Celsius: "))
 
fahrenheit = 9 / 5 * celsius + 32
 
print(f"{celsius}°C is {fahrenheit:.1f}°F")

Check it against a pair you know: 100 must give 212. That single check catches the version where somebody wrote 9 // 5, which is integer division and quietly gives 1.

4. The cost of running something

$\text{cost}=\frac{\text{watts}\times \text{hours}}{1000}\times \text{rate}$

Ask for watts, hours per day, and the price per kilowatt-hour. Print the daily cost and the cost over a 194-day school year.

Answer 4

When it asks, type the watts, the hours per day and the price.

watts = float(input("Power, in watts: "))
hours = float(input("Hours per day: "))
rate = float(input("Price per kWh, in dollars: "))
 
kilowatt_hours = watts * hours / 1000
daily_cost = kilowatt_hours * rate
yearly_cost = daily_cost * 194
 
print(f"Per day:  ${daily_cost:.2f}")
print(f"Per year: ${yearly_cost:.2f}")

kilowatt_hours earns its name here: when the yearly figure looks absurd, that is the line you print to find out whether the error is in the conversion or the multiplication.

5. Averaging, with a guard

The mean of a list of readings is the total divided by how many there are. Write a program that reads numbers until the user types done, then prints the mean — and does not crash when the user types done immediately.

Answer 5

When it asks, type one reading at a time, and done to finish.

readings = []
 
while True:
    entry = input("Reading (or 'done'): ")
    if entry == "done":
        break
    readings.append(float(entry))
 
if len(readings) == 0:
    print("No readings were entered.")
else:
    total = 0
    for reading in readings:
        total = total + reading
    print(f"Mean of {len(readings)} readings: {total / len(readings):.2f}")

The guard is the whole exercise. Dividing by zero is the formula being asked a question it has no answer to, and the program has to answer for it.