Simple Physics Problem please?

Question

The driver of a train travelling at 30,/s applies the brakes when he passes n amber signal. The next signal is 1.5 km down the track and the train reaches it 75 secs later. Assuming a uniform acceleration, find the velocity of the train at the second signal?

Answer 1

What you know: v₀ (=30m/s), d (=1500m), t (=75s)

What you want to know: a

So look for the kinematics equation that relates all of these quantities (see sources):

d = v₀ t + ½(a)(t²)

Solve this for a:

½(a)(t²) = d - v₀ t

a(t²) = 2(d - v₀ t)

a = (2d - 2v₀ t) / t²

Now just plug in the known values:

a = [2(1500) - 2(30)(75)] / (75)²

= (3000 - 4500) / 5625

= -0.267 m/s²

The "-" sign just means that the acceleration is in the direction opposite that of the original motion (i.e. the train is "decelerating").