Aparticle is moving with acceleration a ( t ) = 18 t + 4 . its position at time t = 0 is s ( 0 ) = 8 and its velocity at time t = 0 is v ( 0 ) = 7 . what is its position at time t = 5 ?

Solution:

Given:

a(t) = 18t + 4

at t = 0 :

s(0) = 8

v(0) = 7

where,

s = position of particle

v = velocity of particle

Now, we know the following relations:

a =

v = ∫a dt = ∫(18t + 4)dt = 9 + 4t + C

at t = 0 :

v(0) = 9(0) +4(0) + C

⇒ C = v(0) = 7

⇒ v (t) = 9 + 4t +7

Now, using the relation:

v =

s =  ∫v dt = ∫(9 + 4t +7)dt = 3 + 7t + C

at t = 0 :

s(0) = 3(0) + 2(0) + 7(0) + C

⇒ C = s(0) = 8

⇒ s(t) =  3 + 7t + 8

Now, position at t = 5 :

s(5) =  3 + 7(5) + 8

s = 468

all of the answers are correct.

falsification is manipulating research materials, equipment, or processes or changing or omitting data or results such that the research is not accurately represented in the research record. plagiarism is the appropriation of another person's ideas, processes, results, or words without giving appropriate credit.

explanation:

when insulating materials rub against each other, they may become electrically charged . electrons , which are negatively charged, may be 'rubbed off' one material and on to the other. the material that gains electrons becomes negatively charged. the material that loses electrons is left with a positive charge.