Get premium membership and access questions with answers, video lessons as well as revision papers.

Derive the three equations of linear motion.

      

Derive the three equations of linear motion.

  

Answers


sharon
Consider a body moving in a straight line from an initial velocity u to a final velocity v(u, v?0) within a time t as represented on the graph below:
42320191216.png
The slope of the graph represents the acceleration of the body;
Acceleration, a=(v-u)/t.
Therefore, v=u+at…………………………………. i.
This is the first equation of linear motion.
The area under the graph (area of a trapezium) gives the displacement of the body.
Hence, displacement s= ½(sum of // sides) x perpendicular height between them.
s= ½(u+v)t.
But v=u+at,
Therefore, s=½{u+(u+at)}t
s=½(2u+at)t
Hence, s=ut+½at2……………………………. ii.
This is the second equation of linear motion.
Also, rearranging equation i, we have t=(v-u)/a. substituting this in equation ii, we obtain;
s=ut+½at2=u{(v-u)/a}+½a{(v-u)/a}.
s=u(v-u)/a + a(v-u)2/2a2= u(v-u)/a + (v-u)2/2a
s= {2u(v-u) + (v-u)2}/2a = {2uv-2u2+v2+u2-2uv}/2a
s= {v2-u2}/2a
2as= v2-u2
Hence, v2=u2+2as ……………………………….. iii.
This is the third equation of linear motion.
The three equations hold for any body moving with uniform acceleration.
sharon kalunda answered the question on April 23, 2019 at 09:24


Next: List the characteristics of emotions
Previous: Give examples of methods which can be used to measure distances mention in above I. regular distance ii. irregular distance

View More Physics Questions and Answers | Return to Questions Index


Learn High School English on YouTube

Related Questions