Kinematics refresher (straight-line motion): Which of the following are the standard constant-acceleration equations connecting displacement S, initial velocity u, final velocity v, acceleration a, and time t?

Introduction / Context:For motion along a straight line with constant acceleration, three core equations relate velocity, displacement, time, and acceleration. They are cornerstones in solving a wide range of problems from vehicle braking to projectile components and industrial automation timing.

Given Data / Assumptions:

• Acceleration a is constant in magnitude and direction.
• Variables: initial velocity u, final velocity v, displacement S, time t.
• Straight-line motion; vector signs handled consistently.

Concept / Approach:These equations are derived by integrating a = dv/dt, using v = ds/dt, and applying limits from initial to final states. Because a is constant, the integrals yield closed-form algebraic relations that avoid calculus during routine problem solving.

Step-by-Step Solution:

Verification / Alternative check:Dimensional consistency: a t has velocity units; a t^2 has length units; the relation v^2 − u^2 = 2 a S has dimensions of velocity squared on both sides.

Why Other Options Are Wrong:Each of A, B, and C is correct individually; thus “All of the above” is the comprehensive choice. “None” is inapplicable.

Common Pitfalls:Using these equations when acceleration is not constant; mishandling signs when motion reverses direction during the time interval.

Final Answer:All of the above