Question

With the usual notations, the following equation
$S_t=u+\frac{1}{2}a(2t-1)$ is

• A. Only numerically correct
• B. Only dimensionally correct
• C. Both numerically and dimensionally correct
• D. Neither numerically nor dimensionally correct

Answer 1

Answer: (C)

We can derive this equation from equations of motion.
So it is numerically correct.
$S_t=$ Distance travelled in $t^{\text{th }}$ second
$=\frac{\text{ Distance }}{\text{ Time }}=\left[L{T}^{-1}\right]$
$u=$ Velocity $=\left[L{T}^{-1}\right]$
and $\frac{1}{2}a(2t-1)=\left[L{T}^{-1}\right]$
As dimensions of each term in the given equation are same,
hence equation is dimensionally correct also.