Question

the displacement of a particle S is given by
S=A + BT +CT^2.Deduce the units of the constants A,B and C

Answer 1

If T refers to time:

S = A + Bt + Ct^2

In any equation, all terms on both sides must have the same units. Since we know that this equation gives us the value of 'S', the displacement, all three terms on the right side must also have the units of displacement, i.e, [L].

A is on its own, hence, it has the units of displacement, [L]

Bt must have dimensions [L], and t has dimensions [T]. So, B must have dimensions [L]([T]^-1)

Ct^2 must also have dimensions [L], and t^2 has dimensions [T^2]. So, C must have dimensions [L]([T]^-2)

Answer 2

for example if t is seconds
d = Xi + Vi t - (1/2) g t^2
d is distance, perhaps meters
Xi is then initial location, meters
Vi is initial speed, meters/second
g is acceleration, meters/seconds^2 (about 9.81 m/s^2 on earth)