A particle moves according to a law of motion s = f(t) t ≥ 0 , where t is measured in
seconds and s in feet. f(t) = t 0t 8t 3
2 3 − 1 2 + 4
(a) Find the velocity at time t:
(b) When is the particle at rest?
(c) When is the particle moving in the positive direction?
(d) Find the distance traveled during the first 6 seconds:
(e) Find the acceleration at time t :
(f) When is the particle speeding up? Slowing down?

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

72 is the answer to this problem