We have encountered some equations in an old set of laborato

We have encountered some equations in an old set of laboratory notes, each having two terms on the right-hand side of the equation. We realize we cannot read the final variable or variables listed in each equation. Using dimensions and the equation laws, determine the missing variable from the list below, and if that variable is multiplied or divided. In some questions, more than one variable may be required to form the necessary dimensions. (Enter your answers using the terms given in the table of variable choices. For example if the missing term is

density times heightdensity•height

enter this expression into the answer field. Use positive exponents only.)

Variable choices:

Area

Acceleration

Density

Height

Mass

Speed

Time

Volume

(a)

Speed equals left parenthesis distance right parenthesis divided by left parenthesis time right parenthesis plus left parenthesis acceleration right parenthesisSpeed=(distance)/(time)+(acceleration)

times•

divided by/

(nothing)

Solution

If we consider (a) part here that says

Speed = distance/time + acceleration

According to dimension law,

Only Quantities with same dimensions can be added.

Here, dimension of acceletation is LT^-2. But speed has dimension= LT^-1

Therefore, time must be multiplies with acceleration in right side.

Hence, speed = distance/time + acceleration•time