In the formula s=ut+1/2at square.Make a the subject of formula (b)find the values ot t when s=42,u=2 and a=8.Am getting difficulties in that number.

To make 'a' the subject of the formula s = ut + 1/2at^2, we need to isolate 'a'.

Step 1: Start with the formula s = ut + 1/2at^2.

Step 2: Subtract ut from both sides to move it to the other side of the equation:
s - ut = 1/2at^2.

Step 3: Multiply both sides by 2 to eliminate the fraction:
2(s - ut) = at^2.

Step 4: Divide both sides by t^2:
2(s - ut) / t^2 = a.

So, we have the formula for 'a' as:
a = 2(s - ut) / t^2.

Now let's substitute the values of s = 42, u = 2, and a = 8 into the equation and solve for 't'.

Step 1: Plug in the given values into the formula:
8 = 2(42 - 2t) / t^2.

Step 2: Multiply both sides of the equation by t^2 to eliminate the fraction:
8t^2 = 2(42 - 2t).

Step 3: Distribute the 2 to both terms inside the parentheses:
8t^2 = 84 - 4t.

Step 4: Move all terms to one side of the equation:
8t^2 + 4t - 84 = 0.

Step 5: Simplify the equation:
2t^2 + t - 21 = 0.

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. However, the quadratic equation does not factor nicely, so let's use the quadratic formula.

Step 6: Apply the quadratic formula, which states that the solutions for t can be found using the formula:
t = (-b ± √(b^2 - 4ac)) / (2a).

In our case, a = 2, b = 1, and c = -21.

Step 7: Substitute the values into the quadratic formula and solve for t:
t = (-(1) ± √((1)^2 - 4(2)(-21))) / (2(2)).

Simplifying further:
t = (-1 ± √(1 + 168)) / 4.

Step 8: Calculate the discriminant:
t = (-1 ± √169) / 4.

Since 169 is a perfect square (13^2 = 169), we can simplify:
t = (-1 ± 13) / 4.

Step 9: Calculate the two possible values for t:
t₁ = (-1 + 13) / 4 = 12 / 4 = 3,
t₂ = (-1 - 13) / 4 = -14 / 4 = -3.5.

So, the values of t when s = 42, u = 2, and a = 8 are t = 3 and t = -3.5.

To make "a" the subject of the formula s=ut+1/2at^2, we can start by rearranging it:

s = ut + (1/2)at^2

Move the "ut" term to the other side:

s - ut = (1/2)at^2

Multiply both sides by 2 to eliminate the fraction:

2(s - ut) = at^2

Divide both sides by "t^2":

2(s - ut) / t^2 = a

Therefore, "a" is the subject of the formula:

a = 2(s - ut) / t^2 ---- (Equation 1)

Now, let's use the given values of s=42, u=2, and a=8 to find the values of t.

Substituting these values into Equation 1:

a = 2(42 - 2t) / t^2

Since a=8, we can replace it in the equation:

8 = 2(42 - 2t) / t^2

To simplify further, we can multiply both sides of the equation by t^2:

8t^2 = 2(42 - 2t)

8t^2 = 84 - 4t

Rearrange the equation to obtain a quadratic equation in standard form:

8t^2 + 4t - 84 = 0

To solve this quadratic equation, we can use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

In this case, a=8, b=4, and c=-84. Substituting these values into the quadratic formula:

t = (-4 ± √(4^2 - 4(8)(-84))) / (2(8))

Simplifying further:

t = (-4 ± √(16 + 2688)) / 16

t = (-4 ± √(2704)) / 16

t = (-4 ± 52) / 16

This yields two possible values for t:

t1 = (-4 + 52) / 16 = 48 / 16 = 3

t2 = (-4 - 52) / 16 = -56 / 16 = -3.5

Therefore, when s=42, u=2, and a=8, the possible values for t are 3 and -3.5.