Physics problem with solution please

Question

a bus travels 500m between two stops. is starts from rest and accelerates 1.2m/s^2 until it reaches a velocity of 10m/s. the bus continues with this velocity for a time and then decelerates at 2m/s^2 until it comes to a stop. find the total time required for this journey.

Answer 1

Break this up into three parts - starting, constant speed, and stopping

Starting v = 0 and bus accelerates at a1 = 1.2 m/s^2

It can only accelerate until v1 = 10 m/s so use teh formula

v = at and solve for t using a1 and v1  ---> t1 = v1/a1 = 10/1.2 m/s

Bus covers a distance found by using:

   d1 = (v1^2)/(2a1) = 100/(2.4) m = 41.67 m

SO it has a distance of 500 - d1 = 458.9 m to go.

Now this may seem backward but do the stopping piece next because it is just the opposite of the starting piece and we can get the distacne traveled.

Stopping

Bus goes from 10 m/s to 0 m/s and deccelerates at a2 = -2 m/s

Use  0 = a2t + v1 for find time t, call it t3

t3 = -v1/a2 = -10/(-2) = 5 seconds

And use  x3 = -v1^2/(2a2) = -100/(-4) = 25 m

SO now we know the bus is accelerating or deccelerating fora total distance of:

D = 25 + 41.67 = 66.67 m

and a time of

T = 5 + 8.33 = 13.33 seconds

It still has a distance d = 500 - D = 433.33 m to trave at a speed v1.  Using

d = v1t2  --->  t2 = d/v1 = 43.33sec

So total time is T + t2 = 56.67 sec