How can the first order kinematic (SUVAT) equations be derived?

We start with the following two observations about an object undergoing constant acceleration. First, its acceleration is equal to the change in its velocity over time, hence,

a=(v-u)/t.

Rearranging gives the first SUVAT equation,

v=u+at.

Secondly, we observe that the average velocity of the object is equal to the distance it travels over time. The average velocity of an object undergoing constant acceleration is the average of its initial and final velocities, hence,

(u+v)/2=s/t.

Substituting the value of v in the first SUVAT equation, we have,

(2u+at)/2=s/t.

Rearranging, we have the second SUVAT equation,

s=ut+(at^2)/2.

To derive the third equation, the original equations are rearranged to give,

v-u=at

and

v+u=2s/t.

These equations can be multiplied to give,

(v+u)(v-u)=2as.

Multiplying out the brackets and rearranging gives the third SUVAT equation,

v^2=u^2+2as.

PT
Answered by Peter T. Physics tutor

11920 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

What is the difference between accuracy and precision?


Outline the principal features of a geostationary orbit and use them to explain one use of satellites in this type of orbit.


what is the scape velocity?


Explain the photo-electric effect and describe how the intensity of light effects rate of electron emission.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences