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