To find:
a) The speed of the sprinter while he running
preprekomW
Answered question
2021-08-18
To find:
a) The speed of the sprinter while he running as crossed the finish line
b) After how many seconds was he running at the rate of 10 m per sec
Using the model function where f(t) is the speed of the sprinter per second after t seconds.
Answer & Explanation
mhalmantus
Skilled2021-08-19Added 105 answers
Concept:
Modeling is a method of simulating the real life situations with mathematical equations. Using these models we can forecast the future behavior. We can translate the mathematical word problem into a math expression using variables.
Calculation:
The given model function is
where f(t) is the speed of the sprinter per second after t seconds.
a) The sprinter finished the race in 9.86 seconds.
So, substituting , we het the speed of the sprinter while he crossing the finish line.
Let
Using the calculator, meters per second if rounded to nearest hundredth.
The speed of the sprinter while he running as crossed the finish line is 11.645 m/sec.
b) The speed of the sprinter is given by 10 m/sec.
So,
So,
Divide each side by 11.65,
Using calculator,
Taking natural logarithm on each side, In
Using calculator,
Divide by
Using calculator,
Rounded to nearest hundredth, seconds.
So, after 2.48 seconds his speed was 10 m/sec.
Final statement:
a) The speed of the sprinter while he running as crossed the finish line is 11.65 m/sec.
b) After 2.48 seconds was he running at the rate of 10 m per sec.