State whether the equation $v = u + at^2$ (where $v,u$ are velocities, $a$ is acceleration and $t$ is time) is dimensionally correct. Justify your answer using dimensional analysis.

Question

Accepted Answer

For the equation to be dimensionally valid, **every** term being added must carry the same dimensional formula as $v$ (a velocity), $[LT^{-1}]$.

$[u] = [LT^{-1}]$ — matches, since $u$ is itself a velocity.

$[at^2] = [LT^{-2}]	imes[T^2] = [LT^{0}] = [L]$ — this is a **length**, not a velocity, so it does **not** match $[LT^{-1}]$. …

Q.State whether the equation $v = u + at^2$ (where $v,u$ are velocities, $a$ is acceleration and $t$ is time) is dimensionally correct. Justify your answer using dimensional analysis.

Concept understanding — Dimensional Analysis

Q.State whether the equation v=u+at2v = u + at^2v=u+at2 (where v,uv,uv,u are velocities, aaa is acceleration and ttt is time) is dimensionally correct. Justify your answer using dimensional analysis.

🎓Unlock everything free for 14 days

Q.State whether the equation $v = u + at^2$ (where $v,u$ are velocities, $a$ is acceleration and $t$ is time) is dimensionally correct. Justify your answer using dimensional analysis.

Unlock everything free for 14 days