Make t the subject of formula S = ut + 12at2
A. 1a (-u + U2−2as−−−−−−−−√)
B. 1a {u ± (U2 - 2as)}
C. 1a {u ± 2as−−−√}
D. 1a {-u + (2as)−−−−√}
To make t the subject of the formula S = ut + 12at^2:
1. Move the ut term to the other side by subtracting ut from both sides of the equation:
S - ut = 12at^2
2. Factor out t from the right side of the equation:
S - ut = t(12a - u)
3. Divide both sides of the equation by (12a - u) to isolate t:
t = (S - ut) / (12a - u)
After simplification, the equation becomes:
t = S / (12a - u) - u / (12a - u)
Therefore, none of the options A, B, C, or D accurately represents t as the subject of the formula S = ut + 12at^2.
To make t the subject of the formula S = ut + 1/2at^2, we can follow the steps:
Step 1: Move the ut term to the other side of the equation:
S - ut = 1/2at^2
Step 2: Multiply both sides of the equation by 2 to eliminate the fraction:
2(S - ut) = at^2
Step 3: Expand the left side of the equation:
2S - 2ut = at^2
Step 4: Rearrange the equation to get t^2 alone on one side:
at^2 = 2S - 2ut
Step 5: Divide both sides of the equation by "a" to isolate t^2:
t^2 = (2S - 2ut)/a
Step 6: Finally, take the square root of both sides to solve for t:
t = ± √((2S - 2ut)/a)
Therefore, the correct answer is option B: 1a {u ± (U2 - 2as)}.