Given the following velocity functions of an object moving along a line, find the position function with the given initial position v(t)=2t+4

The position of the particle as a function of times is given by

 where is the position of the particle at t = 0 secs.

Step-by-step explanation:

Give that

we know that

Applying values we get

here 'c' is the constant of integration which represents the position of the particle at time t = 0 secs.

Thus we have

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

c

step-by-step explanation: