SOLUTION: S=ut + at 2 means ( at ) square gives the distance S passed over by a moving body in t s In 4 s the body moves 88 m In 6 s the body moves 168 m Find the values of u and a and

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Question 825871: S=ut + at 2 means ( at ) square
gives the distance S passed over by a moving body in t s
In 4 s the body moves 88 m
In 6 s the body moves 168 m
Find the values of u and a and then find how far the body moves in 5 s.
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--

THE PROBLEM:
The equation S=ut%2B%28at%29%5E2  gives the distance S passed over by a moving body in t sec.
In 4 sec. the body moves 88 m.
In 6 sec. the body moves 168 m.

Find the values of u and a and then find how far the body moves in 5 s.

A SOLUTION:

By substituting the known values for u and a, we can find the exact equation.

When t = 4, S = 88.

S=ut%2B%28at%29%5E2
88=u%284%29%2B%28a%284%29%29%5E2

Simplify.
88=4u%2B16a%5E2
16a%5E2%2B4u=88


When t = 6, S = 168
S=ut%2B%28at%29%5E2
168=u%286%29+%2B+%28a%286%29%29%5E2

Simplify.
168+=+6u+%2B+36a%5E2
36a%5E2%2B6u=168
6a%5E2%2Bu=28

Now we have a system two equations with 2 variables. We can solve for u and a.

Rewrite the first equation in terms of u.
16a%5E2%2B4u=88
4u=-16a%5E2%2B88
u=-4a%5E2%2B22

Substitute -4a%5E2%2B22 or u in the SECOND equation.
6a%5E2%2Bu=168 
6a%5E2%2B%28-4a%5Et%2B22%29=168
6a%5E2-4a%5E2%2B22=28

Simplify.
(((2a^2+22=28}}}
2a%5E2=6
a%5E2=3
a=sqrt%283%29 or a=-sqrt%283%29

Substitute these value for a into the "u=" equation.
u=-4a%5E2%2B22
u=-4%28sqrt%283%29%29%5E2%2B22
u=+-4%283%29%2B22
u=10

a=-sqrt%283%29 will give the same value for u because %28sqrt%283%29%29%5E2=-%28sqrt%283%29%29%5E2.

Now substitute the values for a and u into the original equation.

S=ut%2B%28at%29%5E2
S=%2810%29t%2B%28%28sqrt%283%29%29%5E2%2At%5E2%29
S=10t%2B3t%5E2

Find S when t=5.

S=10%285%29%2B3%285%29%5E2
S=50%2B75
S=125

In 5 sec. the body moves 125 m.

Hope this helps! Feel free to email if you have any questions.

Mrs. Figgy
math.in.the.vortex@gmail.com