Which of the following equations of motion would be used to calculate the displacement given the initial and final velocities as well as the time taken?

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BlackTom AI · Accepted Answer

The question asks which equation of motion would be used to calculate displacement when you know the initial velocity (u), final velocity (v), and the time taken (t).
Option a: v = u + at. This is the formula for final velocity when acceleration is constant, not for displacement directly. It relates v, u, a, and t, but it does not give s unless you also know a. So it’s not the correct choice for displacement with given u, v, and t.
Option b: s = ½(u + v)t. This is the average velocity (u + v)/2 multiplied by time t, which yields the displacement when acceleration is constant and you know the initial and final velocities. Since the time is provided along with u and v, this directly computes s. This aligns with the kinematic relationship for constant acceleration where the displacement equals the average of the velocities times time.
Option c: s = ut + ½at^2. This is the formula for displacement when you know initial velocity u and constant acceleration a, expressed in terms of t. It requires knowing a, which is not given here, and it does not explicitly incorporate the final velocity v. Therefore it’s not the appropriate choice when you have u, v, and t.
Option d: v^2 = u^2 + 2as. This relates velocities to displacement with acceleration a, and it does not involve time t at all. Since the question specifies time as part of the known quantities, this equation does not directly fit the given information for calculating s from u, v, and t.
In summary, among the given options, the equation that directly computes displacement using the initial and final velocities and the time is s = ½(u + v)t, making option b the correct choice.

MUF0121 Physics Unit 1 - Semester 2, 2025

Which of the following equations of motion would be used to calculate the displacement given the initial and final velocities as well as the time taken?

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