Q. If a body moves with uniform acceleration, which physical quantity can be dimensionally derived from s = ut + ½at²?

यदि कोई पिंड एकसमान त्वरण से गति करता है, तो कौन सी भौतिक राशि आयामी रूप से s = ut + ½at² से प्राप्त की जा सकती है?

Velocity
वेग

Force
बल

Distance
दूरी

Time
समय

The equation

s = u t + \frac{1}{2} a t^{2}

is one of the kinematic equations, where

s

represents displacement (a form of distance).

Let's check the dimensions of each term:

$s$ : Dimension is $L$ (Length/Distance).
$u t$ : Dimensions of initial velocity ( $L T^{- 1}$ ) $\times$ time ( $T$ ) = $L$ .
$\frac{1}{2} a t^{2}$ : Dimensions of $\frac{1}{2}$ (dimensionless) $\times$ acceleration ( $L T^{- 2}$ ) $\times$ time squared ( $T^{2}$ ) = $L$ .

Since all terms on the right side of the equation have the dimension of length (

L

), the quantity represented by 's' (the left side) must also have the dimension of length, which corresponds to Distance (or Displacement).

Your support helps keep Exam Achiever 100% free for students preparing for exams.

Thanks for your support!

Your support helps keep Exam Achiever 100% free for students preparing for exams.

Thanks for your support!

Take our Free timed mock tests to sharpen your skills and boost your confidence!