The dimensional formula for acceleration is [M^0 L^1 T^-2], as it is defined as the change in velocity per unit time.
Questions & Step-by-step Solutions
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Q: What is the dimensional formula for acceleration?
Solution: The dimensional formula for acceleration is [M^0 L^1 T^-2], as it is defined as the change in velocity per unit time.
Steps: 6
Step 1: Understand what acceleration is. Acceleration is how quickly something changes its speed or velocity.
Step 2: Recall the formula for acceleration. Acceleration (a) is defined as the change in velocity (Δv) divided by the time (Δt) it takes for that change: a = Δv / Δt.
Step 3: Identify the dimensions of velocity. Velocity (v) is distance (L) divided by time (T), so its dimensional formula is [L^1 T^-1].
Step 4: Substitute the dimensional formula of velocity into the acceleration formula. Since acceleration is velocity divided by time, we have: [L^1 T^-1] / [T^1].
Step 5: Simplify the expression. When you divide [L^1 T^-1] by [T^1], you subtract the exponents of T: [L^1 T^(-1-1)] = [L^1 T^-2].
Step 6: Write the final dimensional formula for acceleration. Since there is no mass involved in the formula, the mass dimension is [M^0]. Therefore, the complete dimensional formula for acceleration is [M^0 L^1 T^-2].
