Question

show that the equations (a) Vf=Vi+at (b) S=Vit+ 1/2 at2 are dimensionally correct

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Answer 1

Here is your answer

Answer 2

Both the equations are kinematics equation which are used for knowing the information of motion of a system.

Explanation:

(a) $v_{f} =v_{i} +at$

Here, $v_{f}$ is the final velocity of the body and $v_{i}$ is the initial velocity of the body. $a$ is the acceleration of body and $t$ is the time take by the body for its motion.

Dimension of left hand side of the above equation i.e.  $v_{f} =[ LT^{-1}]$

Dimension of $v_{i} = [LT^{-1}]$

Dimension of $a=[LT^{-2}]$

And dimension of $t=[T]$

Dimension of right hand side for each term in the above equation i.e. $v_{i}$ and $at$ is $[LT^{-1}]$.

Since dimension of left hand side and right hand side are same, so the equation is dimensionally correct.

(b) $s=v_{i} t+\frac{1}{2} at^{2}$

$v_{i}$ is the initial velocity of the body. $a$ is the acceleration of body and $t$ is the time take by the body for its motion and $s$ is the distance.

Dimension of left hand side of equation i.e. $s$ is $[L]$

Dimension of $v_{i} = [LT^{-1}]$

Dimension of $a=[LT^{-2}]$

And dimension of $t=[T]$

Dimension of right hand side of equation is $[LT^{-1} ][T]+[LT^{-2}] [T][T]=[L]$.

Since dimension of left hand side and right hand side are same, so the equation is dimensionally correct.