Im stuck on this question, plz help Manuel runs a 100-meter race. 6 seconds after the race started Manuel is 40 meters from the starting line and reaches his max speed; he runs at this max speed for the rest of the race. Manuel notices that he is 75 meters from the starting line 11 seconds after the race started.
Suppose Manuel runs for an additional z seconds after reaching his max speed...
What is Manuel's distance from the starting line 6+z seconds after the race started?
What is Manuel's distance from the starting line x seconds after the race started (provided x≥6x)?

Kindly check explanation

Step-by-step explanation:

Given the following :

40 metres covered in 6 seconds

Max speed attained after 6seconds

75 meters covered after 11 seconds

Average Speed for first 40 meters :

Speed = distance / time

Speed = 40m / 6s

Speed = 6.67m/s

To obtain the maximum speed :

Next (75 - 40) meters = 35 meters was covered in (11 - 6)seconds = 5 seconds

Speed at this point is maximum :

Hence, maximum speed = (35m / 5s) = 7m/s

Suppose, Manuel runs for an additional z seconds after reaching max speed :

Distance from starting line 6+z seconds after race started?

Distance after 6 seconds = 40 metres

Distance after z seconds = 7 * z

Total distance = (40 + 7z)

What is Manuel's distance from the starting line x seconds after the race started (provided x≥6x)?

Distance for first 6 seconds = 40 meters + distance covered after 6 seconds = (7 * (x-6))

40 + 7(x - 6)

Eureka!

He discovered that the amount of liquid displaced when an object is submerged in the liquid is the *same* as the one of the object. It does not need to sink. For instance, Archimedes got in the bath tub and the water spilled off, he thought Eureka! Why?

The King of Syracuse wanted to know whether a crown forged for himself was all made of gold or had been mixed with something else. He did not want to break the beautiful crown. No one knew.

Archimedes went back to palace (the legend says naked because of his excitement), put the crown in a barrel with water, measure the volume of water displaced, and derive the density of the crown (having measured its weight). the density was different than the one of gold.

The king broke the crown and indeed found it was an alloy! The goldsmith was ... killed :(