show the expression v=at is dimensionally correct where v represents speed an acceleration and t is instant time?
To check if the expression v = at is dimensionally correct, we need to ensure that the dimensions on both sides of the equation are the same.
Let's break down the dimensions of each variable:
v represents speed, which has the dimensions of length divided by time (L/T).
a represents acceleration, which has the dimensions of length divided by time squared (L/T^2).
t represents time, which has the dimensions of time (T).
Now let's substitute these dimensions into the equation:
On the left-hand side, v has the dimensions of L/T.
On the right-hand side, a multiplied by t results in (L/T^2) × T = L/T.
Since both sides of the equation have the same dimensions (L/T), the expression v = at is dimensionally correct.
To summarize:
- Speed has the dimension of L/T.
- Acceleration has the dimension of L/T^2.
- Time has the dimension of T.
- By substituting these dimensions into the expression v = at, we find that both sides have the same dimension of L/T, confirming that the equation is dimensionally correct.