Question

Which one of the following equations represents the motion of a body with finite constant acceleration. In these equations $y$ denotes the displacement of the body at time $t$ and $a,b$ and $c$ are constants of motion

• A. $y=at$
• B. $y=at+b{t}^2$
• C. $y=at+b{t}^2+c{t}^3$
• D. $y=\frac{a}{t}+bt$

Answer 1

The correct option is B $y=at+b{t}^2$

As acceleration is constant so $\frac{dv}{dt}=k$
Where $k$ is cobstant
$\Rightarrow v=kt+c$
$\Rightarrow \frac{dy}{dt}=kt+c$
$\Rightarrow y=\frac{1}{2}k{t}^2+ct$
Only option B satisfies the above condition rest all have either zero or non-uniform acceleration