A train is moving with an initial velocity of 30m/s the brakesapplied to produce retardation of 1.5 m/s calculate the time when it comes to rest

assuming you meant 1.5 m/s^2, then it will of course take

(30m/s)/(1.5 m/s^2) = 20 s

Think about it. If it loses velocity by 1.5 m/s every second, wit will take 20 s to lose all 30 m/s.

V = Vo + a*t = 0,

30 + (-1.5)t = 0,
t = 20 s.

To calculate the time it takes for the train to come to rest, we can use the equation of motion:

v^2 = u^2 + 2as

Where:
v = final velocity (0 m/s since the train comes to rest)
u = initial velocity (30 m/s)
a = acceleration (retardation in this case, -1.5 m/s^2)
s = distance traveled

Plugging in the values, the equation becomes:

0^2 = 30^2 + 2(-1.5)s

Simplifying:

0 = 900 - 3s

Rearranging the equation to solve for s:

3s = 900

s = 900 / 3

s = 300 m

Now we can use the equation of motion:

v = u + at

Where:
v = final velocity (0 m/s)
u = initial velocity (30 m/s)
a = acceleration (retardation in this case, -1.5 m/s^2)
t = time

Plugging in the values, the equation becomes:

0 = 30 + (-1.5)t

Rearranging the equation to solve for t:

-1.5t = -30

t = -30 / -1.5

t = 20 seconds

So, it takes 20 seconds for the train to come to rest.