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

Question

BlackTom AI · Accepted Answer

To approach this question, I’ll examine what each equation represents and when it is used.
Option a: s = ½(u + v)t. This is the average velocity multiplied by time. It gives displacement if acceleration is not explicitly needed, but it assumes constant acceleration and uses average velocity; however, it does not directly incorporate acceleration a or the relation between u and v in terms of a. It’s not the standard equation for displacement when you know initial and final velocities together with acceleration.
Option b: v = u + at. This is the equation that links initial velocity, final velocity, acceleration, and time. It is useful when time t is known, but the question asks for displacement, not velocity as a function of time, and time is not provided here, so this one doesn’t directly yield displacement using the given information.
Option c: s = ut + ½at^2. This is the displacement formula derived from integrating velocity with respect to time, given initial velocity u and constant acceleration a, with time t. It does give displacement, but it requires time t as a variable. Since the problem mentions initial and final velocities and acceleration, not time, this form is not the most direct for the given data.
Option d: v^2 = u^2 + 2as. This equation directly relates the squares of the velocities to displacement and the accelerative term, without needing time. It is derived from kinematics by eliminating time and is specifically the relation between initial velocity u, final velocity v, acceleration a, and displacement s. Since the question asks for displacement given initial and final velocities and acceleration, this equation is perfectly suited.
In summary, the key idea is to match the unknown (displacement) with an equation that directly connects u, v, a, and s without requiring time. Among the provided forms, option d exactly provides that direct relation, whereas the other options either require time or describe displacement in a way that doesn’t align with the given data.

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 acceleration?

View Explanation

Log in for full answers

Similar Questions

An automobile of mass 2000 kg moving at 20 m/s is braked suddenly with a constant braking force of 10,000 N. How far does the car travel before stopping?

What is the meaning of subscript i in vi and subscript f in vf?

What is the difference between average and instantaneous velocity?

What is the difference between velocity and acceleration?

What is a motion?

Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed of twice as high as Bill's ball. The maximum height of Joe's ball will be

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?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler