$1$a

$$ Dimensional analysis can be used to verify whether formulae are dimensionally valid or not. Produce a single page training document which explains this for the $3$ equations shown below and indicate if they are dimensionally valid or NOT.

Note that u and v are velocities, a is an acceleration, s is a distance, t is a time and F is force.

Your personal value B $=12$

$1)($B$)$s $=(2($B$))($u$+$v$)$t$2$

$2)$ v$2=$ u$2+4$as

$3)($B$)$F $=$ ma

$$ A client of your company extracts oil from the North Sea. They use CNC machines to produce drill bits in their factory.

Select an appropriate AP $($arithmetic progression$)$ equation $($not from those above$)$ and demonstrate how you would estimate the cost of boring a hole $10$x$(12)$m deep if the cost is $150$ for drilling the $$rst metre with an increase in cost of $10$ per metre for each succeeding metre drilled.