IDNLearn.com is your go-to platform for finding reliable answers quickly. Join our community to receive timely and reliable responses to your questions from knowledgeable professionals.

derive the formula v= u+ at
please derive in detail ​


Sagot :

Lets do

We know

The rate of change of velocity is acceleration .

[tex]\\ \sf\longmapsto a=\dfrac{dv}{dt}[/tex]

[tex]\\ \sf\longmapsto dv=adt[/tex]

Integrate both sides

[tex]\\ \sf\longmapsto \int dv=a\int dt[/tex]

As acceleration is constant .Take it outside of integral .On velocity we can take limit u to v and time from 0 to t

[tex]\\ \sf\longmapsto {\displaystyle{\int}}^v_u dv=a{\displaystyle{\int}}^t_0 dt[/tex]

Hence

[tex]\\ \sf\longmapsto v{\huge{|}}^v_u=at[/tex]

[tex]\\ \sf\longmapsto v-u=at[/tex]

[tex]\\ \sf\longmapsto v=u+at[/tex]