How to rearrange physics formulas to find acceleration, velocity, or time?

Rearranging physics formulas requires systematic algebraic manipulation while preserving equation balance—whatever operation you perform on one side must be done to the other. For the basic formula v = u + at, solving for acceleration means isolating a: subtract u from both sides to get v - u = at, then divide by t to yield a = (v - u) / t. To solve for time, again subtract u (v - u = at), then divide by a: t = (v - u) / a. Each rearrangement follows the same principle: use inverse operations (subtraction for addition, division for multiplication) to move unwanted terms away from your target variable.

For more complex formulas like s = ut + ½at², solving for acceleration requires extra steps because a appears inside a product and multiplied by a fraction. First, subtract ut from both sides: s - ut = ½at². Then multiply by 2 to clear the fraction: 2(s - ut) = at². Finally, divide by t²: a = 2(s - ut) / t². This multi-step process requires patience and careful order of operations—attempting to divide by t² before clearing the ½ coefficient creates unnecessary complexity.

For quadratic equations like solving the same formula for time, you'll need the quadratic formula. Rearrange to standard form: ½at² + ut - s = 0, multiply by 2: at² + 2ut - 2s = 0. Apply the quadratic formula with coefficients A=a, B=2u, C=-2s: t = [-2u ± √(4u² + 8as)] / 2a = [-u ± √(u² + 2as)] / a. The ± symbol yields two solutions; choose the positive one since negative time is non-physical in these contexts. Practicing these rearrangements with different formulas builds algebraic confidence essential for physics problem-solving, where rarely does a formula come in the exact form you need.