Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

If $x = at + bt^2$ , where $x$ is the distance travelled by the body in kilometres while $t$ is the time in seconds, then the units of $b$ are

km/s

km-s

km/s $^2$

km-s $^2$

Principle of Homogeneity: According to the principle of homogeneity of dimensions, physical quantities can only be added or subtracted if they have the same dimensions. This means that in the equation $x = at + bt^2$ , each term on the right-hand side ( $at$ and $bt^2$ ) must have the same physical dimensions as the term on the left-hand side ( $x$ ) .
Dimensional Analysis:

The quantity $x$ represents distance, so its unit is kilometres (km) and its dimension is Length [L].
The quantity $t$ represents time, so its unit is seconds (s) and its dimension is Time [T].
For the term $bt^2$ to have the same dimensions as $x$ , the units must satisfy the equation: $\text{Unit}(b) \times \text{Unit}(t)^2 = \text{Unit}(x)$ $\text{Unit}(b) \times \text{s}^2 = \text{km}$

Calculation: Solving for the unit of $b$ : $\text{Unit}(b) = \frac{\text{km}}{\text{s}^2}$
Conclusion: The unit of $b$ is km/s $^2$ .

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