Question

if x= a+bt+ct², where x is in metres and t in seconds, what is the unit of c?

Answer 1

First look at this example
5m + 7kg = ?
Can you add? No. Not possible. Also, it’s meaningless.

However,
5m + 7m = 12m
It’s possible

So, in addition all the terms should have same units.
_______________

x = a + bt + ct²
To add the terms a, bt and ct² all should have same units. Also, all should have units of metre because x is in metres.

So,
ct² = metre
c (second)² = metre
c= metre / second²

∴ Unit of c is m/s²