The volume of an object as a function of time is calculated by v = At3+B÷t where t is time measured in seconds and v is in cubic metres. Determine the dimension of the constants A and B.

A = m³/s³ = [L]³/[T]³ = [L³T⁻³]

B = m³s = [L³T]

Explanation:

We have the equation:

V = At³ + B/t

where, the dimensions of each variable are as follows:

V = m³ = [L]³

t = s = [T]

substituting these in equation, we get:

m³ = A(s)³ + B/s

for the homogeneity of the equation:

A(s)³ = m³

A = m³/s³ = [L]³/[T]³ = [L³T⁻³]

Also,

B/s = m³

B = m³s = [L³T]

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s