Newton’s law of cooling states that dx dt = −k(x − a) where x is the temperature, t is time, a is the ambient temperature, and k > 0 is a constant. suppose that a = a0 cos(ωt) for some constants a0 and ω. that is, the ambient temperature oscillates (for example night and day temperatures). a) find the general solution. b) in the long term, will the initial conditions make much of a difference? why or why not?

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