Question

With the usual notations , check if the following equation `S_(t) = u + (1)/(2) a ( 2t -1)` is dimensionally correct or not.

Answer 1

Given `s_(t)` = distance travelled by the body in t th second. `= [ LT^(-1)]`,
a = Acceleration `= [LT^(-1)]`,
v = velocity `= [ LT^(-1)]`,
` t= time = [T]`
By substituting the dimension of each quantity , we can check the accuracy of the formula
`S_(t) = u + (1)/(2) a ( 2t -1) :. [LT^(-1) = [LT^(-1) + [LT^(-2)] [T]`
`rArr [LT^(-1)] = [LT^(-1) + [LT^(-1)]`
Since the dimensions of each term are equal , therefore, this equation is dimensionally correct. And after derving this equation from kinematics , we can also proove that this equation is correct numerically also.