Make t subject of the formula: s=ut+1/2at^2.
By using completing the square method amd also apply all the rule involve to it. hence, you will get
t=-u+/- sqrtu^2+2as/a
use the quadratic formula. It might help to get rid of the fraction first
at^2 + 2ut - 2s = 0
t = (-2u ±√(4u^2 + 8as))/(2a)
= (-u±√(u^2+2as))/a
To make t the subject of the formula s = ut + 1/2at^2, we will isolate the term with t on one side of the equation.
Starting with the given equation:
s = ut + 1/2at^2
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) = 2 * (1/2at^2)
2s - 2ut = at^2
Step 3: Move the term containing t^2 to one side of the equation:
at^2 = 2s - 2ut
Step 4: Divide both sides of the equation by a:
(at^2)/a = (2s - 2ut)/a
Step 5: Simplify:
t^2 = (2s - 2ut)/a
Step 6: Divide both sides of the equation by 2u:
t^2 / 2u = (2s - 2ut)/ (2u)
Step 7: Simplify:
t^2 / 2u = s - ut
Step 8: Move the -ut term to the other side of the equation:
t^2 / 2u + ut = s
Step 9: Factor out t from the second term on the left-hand side:
t^2 / 2u + 2ut / 2u = s
Step 10: Combine the terms on the left-hand side:
(t^2 + 2ut) / 2u = s
Step 11: Multiply both sides of the equation by 2u to isolate t:
t^2 + 2ut = 2us
Step 12: Rearrange the terms to get t as the subject:
t^2 + 2ut - 2us = 0
t^2 + 2ut - 2us = 0 is the equation with t as the subject of the formula s = ut + 1/2at^2.
To make "t" the subject of the formula "s = ut + (1/2)at^2," you need to isolate "t" on one side of the equation by performing a series of algebraic steps. Here's how you can do it:
Step 1: Start with the given formula: s = ut + (1/2)at^2.
Step 2: Begin by isolating the term with "t" on the right side of the equation. Subtract "ut" from both sides of the equation:
s - ut = (1/2)at^2.
Step 3: Since "t" is present in the term on the right side, we need to eliminate the "(1/2)a" factor next to "t^2." To do this, we divide both sides of the equation by "(1/2)a":
(s - ut) / [(1/2)a] = t^2.
Step 4: Simplify the right side of the equation. One way to do this is by multiplying both sides by 2a:
2a((s - ut) / [(1/2)a]) = 2at^2.
This simplifies to:
2(s - ut) / [(1/2)a] = 2at^2.
Step 5: Continue simplifying by canceling common factors. On the left side, cancel the "2" and "(1/2)" factors:
(s - ut) / a = 2at^2.
Step 6: Multiply both sides of the equation by "a" to eliminate the fraction:
(s - ut) = 2at^2.
Step 7: To isolate "t," subtract "s" from both sides of the equation:
(s - ut) - s = 2at^2 - s.
This simplifies to:
-ut = 2at^2 - s.
Step 8: Divide both sides by "-u" to solve for "t":
(-ut) / (-u) = (2at^2 - s) / (-u).
This results in:
t = (2at^2 - s) / (-u).
Therefore, "t" is the subject of the formula when rewritten as:
t = (2at^2 - s) / (-u).