Question

The velocity of a particle increases from u to v in a time t during which it covers a distances S. If the particle has a uniform acceleration, which one of the following equations does not apply to the motion?

• A. 2 S = (v + u) t
• B. $a=\frac{v-u}{t}$
• C. $v^2=u^2-2aS$
• D. $S=[u+\frac{1}{2}at]t$

Answer 1

The correct option is C $v^2=u^2-2aS$

$\frac{dv}{dt}=a$

by integrating once we get $v-u=at$ i.e. option B.

also $\frac{ds}{dt}=v$ so integrating once more we get $S=ut+\frac{1}{2}a{t}^2$ i.e. option D

by using $v=u+at$ and $ expression of S can be converted to A.

now eleminating t from equation in option A and option B we will get

and expression $v^2-u^2=2as$ but in option C where $v^2-u^2=-2aS$ so expression in option C is not correct so answer is option C.