This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Define average velocity. For an object moving with constant acceleration, the average velocity (v) is the arithmetic mean of its initial velocity (u) and final velocity (v). v = (u+v)/(2) Step 2: Relate displacement to average velocity and time. Displacement (S) is the product of average velocity and time (t). S = vt Substitute the expression for v from Step 1 into this equation: S = ((u+v)/(2))t Step 3: Use the first equation of motion. The first equation of motion states that the final velocity (v) is equal to the initial velocity (u) plus the product of acceleration (a) and time (t). v = u + at Step 4: Substitute the expression for v into the displacement equation. Substitute v = u + at into the equation for S from Step 2: S = ((u + (u+at))/(2))t Step 5: Simplify the expression. S = ((2u+at)/(2))t S = ((2u)/(2) + (at)/(2))t S = (u + (1)/(2)at)t Distribute t: S = ut + (1)/(2)at^2 This is the required kinematic equation. The derived equation is: S = ut + (1)/(2)at^2 That's 2 down. 3 left today — send the next one.