Question

Find the dimension of Aand B in the expression F=At^2 +Bt where F=force and T=time

Answer 1

Answer:

Dimensions of A and B are,

A=M¹L¹T^-⁴

B=M¹L¹T^-3

Answer 2

Answer:

We know that,

$F=ma\\ =>F=m(\frac{v-u}{t})\\ =>F=\frac{mv-mu}{t}\\ =>F=\frac{mv}{t}-\frac{mu}{t}\\ =>F=\frac{mv}{t^{3}}×t^{2}-\frac{mu}{t^{2}}×t$

Comparing with F=At^2+Bt, we get,

$A=\frac{mv}{t^{3}}=\frac{m×\frac{S}{t}}{t^{3}}=\frac{mS}{t^{4}}\\ and\: B=\: -\frac{mu}{t^{2}}=\: -\frac{m×\frac{s}{t}}{t^{2}}=\: -\frac{ms}{t^{3}}$

Dimensional unit of A= $[M^{1}L^{1}T^{-4}]$

Dimensional unit of B= $[M^{1}L^{1}T^{-3}]$