The function v(t)=-9.8t+5 gives the instantaneous velocity of an object thrown upward with an initial velocity of 5 m/sec. at what time t does the object start falling?

0.5 s   (using 1 significan figure since the initial velocity is given with 1 significant figure)

Explanation:

Let's see what each term in the function v (t) = - 9.8t + 5 means:

Term: - 9.8 t

        The variable t is the time

        The coffecient - 9.8 (which is negative) means that the velocity is reduced 9.8 m/s each second.

        That means that the motion is uniformly decelerated with acceleration - 9.8 m/s².

Term + 5

        The term + 5, means that the object was launched with an upward velocity of 5 m/s.

Hence the equation tells that after the object was launched upward it starts to lose speed and will reach a maximum height when the velocity is equal to zero, from which it starts falling.

So, you can calculate when the object reachs it maximum height and starts falling by making the velocity, v (t), equal to zero and solving for t. This is how you do it:

v (t) = 00 = - 9.8t  + 5 9.8t  = 5               remember that the units of 9.8 is m/s² and of 5 is m/st = 5 m/s / 9.8 m/s² = 0.51 s

So, the object starts fallin at 0.51 s. Since, the velocity is reported with 1 significant digit you answer should also show 1 significant digit, which means t = 0.5 s.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

6/ 11 = 0.545454 so your answer is55%