Question

In the SI unit system, time (t) is measured in seconds, distance (d) is measured in meters, velocity (v) is measured in meters per second, and acceleration (a) is measured in meters per second squared.

Based on these units, select any of the following expressions that could be valid expressions?
1- t=cubed rootinside d^2/va
2- v=at
3- a=sqrt vd/t^3
4- d=at
5- v=a/t
6- a=d/t^2

Answer 1

1) t=cubed rootinside d^2/va

2) v=at

3) a=sqrt vd/t^3

6) a=d/t^2

Explanation:

We are given the following:

In the SI unit system, time (t) is measured in seconds(s),

distance (d) is measured in meters(m)

velocity (v) is measured in meters per second
`(ms^(-1))`, and

acceleration (a) is measured in meters per second squared
`(ms^(-2))`.

`\text{Velocity} = \frac{\text{Distance}}{\text{Time}}\\\\\text{Acceleration} = \displaystyle\frac{\text{Change in velocity}}{\text{Time}}\\\\1)\\\\t = ((d^2)/(va))^{(1)/(3)}\\\\t = ((m^2)/(ms^(-1)ms^(-2)))^{(1)/(3)}\\\\t = (s^3)^{(1)/(3)}\\\\t = s\\2)\\v = at\\v = ms^(-2)* s\\v = ms^(-1)\\\\3)\\a = \sqrt{(vd)/(t^3)}\\\\a = \sqrt{((ms^(-1))(m))/(s^3)}\\\\a = \sqrt{m^2s^(-4)} = ms^(-2)\\\\6)\\a = (d)/(t^2)\\\\a = (m)/(s^2) = ms^(-2)`

Thus, valid expressions are

1) t=cubed rootinside d^2/va

2) v=at

3) a=sqrt vd/t^3

6) a=d/t^2