Question

The distance, x, covered by a particle in time, t, is given as x=a +bc+ct^2 +dt^3

.find the dimension of the constants a, b, c and d​

Answer 1

`a` has units of distance

`b` has units of distance over time

`c` has units of distance over
`time^2`

`d` has units of distance over
`time^3`

Step-by-step explanation:

Since the expression for the distance is:

`x = a+b\,t+c\,t^2+d\,t^3`

then:

`a` has units of distance

`b` has units of distance over time

`c` has units of distance over
`time^2`

`d` has units of distance over
`time^3`

because we are supposed to be able to add all of the terms and get a distance. So the products on each term that contains factors of time (t) should be cancelling those time units with units in the denominator of the multiplicative constant s that accompany them.