Question

Consider the following quantities: distance x, velocity v, acceleration a, and time t. Which of the following are dimensionally consistent?

1) x and v
2) v and a
3) a and t
4) x and t

Answer 1

Distance and time, velocity and acceleration, and acceleration and time are dimensionally consistent.

Step-by-step explanation:

Dimensional consistency means that the dimensions of each quantity in an equation are the same on both sides of the equation. Let's consider each option:

1. x and v: distance x has dimension L (length) and velocity v has dimension LT-1 (length/time). These dimensions are not consistent, so option 1 is not dimensionally consistent.
2. v and a: velocity v has dimension LT-1 and acceleration a has dimension LT-2 (acceleration is the rate of change of velocity). These dimensions are consistent, so option 2 is dimensionally consistent.
3. a and t: acceleration a has dimension LT-2 and time t has dimension T (time). These dimensions are consistent, so option 3 is dimensionally consistent.
4. x and t: distance x has dimension L (length) and time t has dimension T (time). These dimensions are consistent, so option 4 is dimensionally consistent.

Therefore, options 2, 3, and 4 are dimensionally consistent.