Solve .5m/s^2(t^2)=6m/s(t)-25m Kinematics Equation

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To solve the kinematics equation 0.5m/s²(t²) = 6m/s(t) - 25m, it's important to avoid dividing by t, as it alters the equation. Instead, rearranging the terms leads to the quadratic form 0.5t² - 6t + 25 = 0. The quadratic formula can then be applied with a = 0.5, b = 6, and c = 25 to find the values of t. This will yield two potential solutions, but only one will be valid, as negative time is not physically meaningful. Properly applying the quadratic equation is essential for finding the correct time value.
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k so kinematics equations set equal..have to solve..
.5m/s^2(t^2)=6m/s(t)-25m

so i divided all by t to get

.5m/s^2(t)=6m/s-25
...?
 
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You can't divide 25m by t and get 25. You should leave the terms as is, move everything over to one side and use the quadratic equation to solve for t.
 
my mistake there is still supposed to be a unit..i just did that to get rid of the one t and make the other one just t instead of t^2
then if i move everything it will be...
thats where I am stuck

t=12s-25m
 
No, you have to leave it as it was. Then move everything over and you get

.5t^2 - 6t + 25 = 0

Now, use the quadratic equation where a = .5, b = 6 and c = 25 to solve for t. You should get two answers, only one will be correct. It's possible one will be negative, and that one will not work.
 

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