Can you solve with the answers, which are given?

Question

The distance traveled by a 75 mph train in 2 hours is 150 miles.
Compare each question with the information above.
a) Begining at a standstill, a car maintains a constant acceleration of 10 ft/sec^2 for 10seconds. What is its velocity after 10seconds? Give your answer in ft/sec and then convert in to mi/h.
b) In a vacuum, light travels at a speed of 300,000 kilometers per second. How many kilometers does it travel in a year? (This distance equals one light-year.)
c) A long distance runner ran in 5 hours, avering 6 mph for the first 3 hours and 5 mph for the last 2 hours. How far did she run?
This is a calculus problem. Please explain the answer in detail if you can.
This is a calculus problem.
I have answers, but I don't know how to get those answers.
(a) 100 ft/sec = 68.08mph
(b) 9.46*10^12 km
(c) 28 miles

Answer 1

You don't need calculus to do any of these questions.

a) Acceleration is constant at 10 ft/sec^2. This means that after N seconds, your speed is N sec*10 ft/sec^2. The seconds cancel out -- so your speed is 10N sec. n 10 seconds, your speed is 10*10 ft/sec = 100 ft/sec.

To convert to MPH, multiply by 3600 (the number of seconds in an hour) and divide by 5280 (the number of feet in a mile). This gives you 68.18182

b). You are told tha tthe speed of light is 300,000 k/sec. To find out how far it travels in a year, multiply this by the number of seconds in a year.

# Seconds in a year = 60*60*24*365.25 = 31,557,600.

Multiply this times 300,000 km to get:

9,467,280,000,000 km

c. She runs for three hours at 6 mph -- so in the first three hours she goes 18 miles (3*6). Then she runs for two hours at 5 mph (so goes an additional 10 miles). 18+10 = 28/

See -- no Calculus.