Question

Can someone help me? This problem is worth 20 points towards my next exam :(

A bus starts from rest and accelerates at 2 m/sec2 until it reaches a velocity of 12 m/sec. The bus continues at this velocity for a period of time and then decelerates at 2.5 m/sec2 and comes to a stop 900 m. from it’s starting point. How much time did the bus take to travel the 900 m?

Answer 1

First part of trip:
a = 2 m/s^2
Vi = 0 m/s
Vf = 12 m/s
Xi = 0
Xf = ?
t = ?

Now, find the unknowns. Since it's constant acceleration, to calculate the time it took to get to 12m/s use the formula:
Vf = Vi + a*t
12 m/s = 0 m/s + (2 m/s^2) * t
t = 6 seconds

Now see how far it went in those 6 seconds:
Xf - Xi = Vi * t + .5a * t^2
Xf - 0m = 0 m/s + .5(2m/s^2)(6s^2)
Xf = 36m

900m - 36m = 864m to go...

Now you need to figure out how long it will take it to slow down if it's going 12m/s with a deceleration of -2.5m/s^2.
a = -2.5 m/s^2
Vi = 12 m/s
Vf = 0 m/s
Xi = 0
Xf = ?
t = ?

Similar to before:
Vf = Vi + a * t
0m/s = 12m/s + (-2.5m/s^2)*t
t = 4.8s

Now see how far it took it to stop:
Xf - Xi = Vi * t + .5a * t^2
Xf - 0m = 12m/s * 4.8s + .5(-2.5m/s^2)(4.8s^2)
Xf = 28.8m

So, so how much distance is left?
900m - 36m - 28.8m = 835.2m

It was going 12 m/s for the entire time it took it to go 835.2m...so it took it:
(835.2m)/(12m/s) = 69.6 seconds

Add up the times to get the final answer:
69.6s + 6s + 4.8s = 80.4s

Yep, I can see why this one was extra credit :P

Answer 2

Thank you so much! I finally get it now :) my professor made us buy a cheap 20 dollar physics book that has all the examples but doesn't show the work and how they got the answer :( thanks again, you're a life saver!

Answer 3

Glad to help :)