Question

If s =at^2+bt +c then find the value of [ds/dt]t= 1​

Answer 1

Answer:

Let [x] = dimension of “x”.

If s = a . t^2 + b . t + c

Then [s] = [a.t^2 + b.t + c]

So [s] = [a.t^2] + [b.t] + [c]

Therefore

[s] = [a.t^2] = [a] . {t]^2

[s] = [b.t] = [b] . [t]

[s] = [c]

Since [s] = L (length, distance, space) and [t] = T (time)

It follows

L = [c] … [c] = L <answer 3>

L = [b] . T … [b] = L/T <answer 2>

L = [a] . T^2 … [a] = L/T^2 <answer 1>

SI units (my recommendation):

{c} = {L} = m (meter)

{b} = {L/T} = m/s (meter per second - velocity)

{a} = {L/T^2} = m/s^2 (meter per squared second - meter per second per second - acceleration)

Is your child scared of Maths?

The rule is that all the units of an addition or subtraction must be the same. You can’t add different things together.

Since “s” is a distance, all the units of the three terms on the right hand side must resolve to meters.

So “a” must have units so that when we multiply it by seconds 2 we end up with m.

“b” must have units that will give meters when we multiply it by seconds (so those seconds must “cancel.”)

And “c” must be meters.

This is a standard thing you need to be able to figure out on your own.