Question

The position x of a particle depends upon time t according to the equation x = at + bt². Determine the dimensions and units of a and b. What are the physical quantities denoted by a and b?

Answer 1

The dimension of $a$ is $[LT^{-1}]$ and dimension of $b$ is $[LT^{-2}]$.

The units of $a$ is $m/s$ and units of $b$ is $m/s^2$.

Hence, $a$ denotes the velocity of the particle and $b$ denotes the acceleration of the particle.