# Total time travelled

phynaive

## Homework Statement

a bus starts from rest and accelerating at 1.5m per second squared until it reaches a velocity of 9m/s.The bus continues at this velocity and then decelerates at -2m per second squared until it comes to a stop. 400m from its starting point. How much time did the bus take to cover the 400 m?

## Homework Equations

s =vt, v=u+at, s= ut+ 1/2 * at^2, v^2= u^2 + 2as

## The Attempt at a Solution

intially found out the time traveled until it reaches 9m/s. so starting from rest, u=0, substituting in 2nd eq. I got t= 9sec. After this I am totally confused. I found out the initial distance travelled, and final diatance traveled . I know somewhere I am doing wrong. Please help me solving this problem.

RoryP
it appears this problem could be split into different sections, try to find out what you can about the bus in each of these sections, then see where that takes you

RoryP
also do you have the answers so we can see what we are aiming for?
i would also check the time you got for substituting u=0 and a=1.5, i didnt get t=9.

phynaive
The time taken to reach 9m/s with a= 1.5m/s^2 is v=u+at => 9= 0+1.5t => t ( initial)= 6sec.
the initial distance traveled to reach from 0 to 9m/s with a =1.5 and t =6 is s= ut+i/2 at^2

=> the distance s(initial)= 0+1/2 * 1.5 * 6*6 = 27.

The time taken to stop from u= 9m/s with a = -2m/s^2, v =0 is v= u+at => t (final)= 4.5sec.

The final distance traveled when the bus was decelerating before stop with v=0,
u=9m/s, a -2m/s^2 is v^2 = u^2 +2as => s( final)= 20.25m

So the distance traveled with 9m/s continuously= total distance- s(initial)-s(final)
=> 400-27-20.25= 352.75m

the time taken to travel 352.75 m with the velocity 9m/s is t= s/v = 352.75/9= 39.19 sec

so the total time = t (initial)+ t ( final) + t = 6+4.5+39.19 = 49.69 sec

But in the textbook the answer was given as 50 sec.

Please let me know where I have done wrong

RoryP
yeah i got the same asnwer!
well the textbook has obviously rounded the answer to the nearest second that's all!
well done =]

phynaive
Thank you RoryP

3.211k
Looks like you already solved this, good job. Using different words to do the same thing:

|---1----->|---2--------->|---3------->|

So you found t1 = 6
And you found that t3 = 4.5

Instead of d = vt + .5at^2 to find d1 and d3, you can also use average velocity. Vave= (v + v')/2 .

So Vave1 = 4.5 m/s , Vave2 = 9 m/s , and Vave 3 is 4.5 m/s .

d = (Vave1)(time1) + Vave2(time2) + Vave3(time3)

You can solve for time2 and add it with t1 and t3 from above to get 49.69 s.