Do you understand volume flow rate? determine the time required for a 50-l container to be filled with water when the speed of the incoming water is 25 cm/s and the cross-sectional area of the hose carrying the water is 3 cm2.

666.67 s

Explanation:

Q = AV(1)

Where Q=Volume of flow rate (m³/s), A=cross sectional area occupied by the flow rate(m²), V=Average velocity of flow(m/s).3

Give:A=3 cm²

and  to convert from cm³ to m² (divide by 10000),

∴ A=3/10000=0.0003m²

And V=25cm/s

and  to convert from cm/s to  m/s (divide by 100),  

∴V=25/100(m/s) = 0.25m/s.

∴ Q=0.0003×0.25 = 0.000075m³/s.

Also, Q = V/t (2)

Where V=Volume of the container to be filled with water (m³)

t= Time take to fill the container (seconds).

making t, the subject of formula in equation 2,

t= V/Q

Given: V= 50L,  to convert from L to m³ (divide by 1000)

∴V= 50/1000= 0.05m³.

And Q=0.000075m³/s.

∴ t= 0.05/0.000075

⇒ t= 666.666667

approximating to 2 decimal place.

∴   t = 666.67 s

current flows in a wire

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