SOLUTION: Find the time it takes to travel 30km for a bus which accelerates uniformly from 40km/hr to 80km/hr. Show your solution.

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Find the time it takes to travel 30km for a bus which accelerates uniformly from 40km/hr to 80km/hr. Show your solution.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1184351: Find the time it takes to travel 30km for a bus which accelerates uniformly from 40km/hr to 80km/hr. Show your solution.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the time it takes to travel 30km for a bus which accelerates uniformly
from 40km/hr to 80km/hr. Show your solution.
~~~~~~~~~~~~~~~ 


You are given:  initial velocity  v%5B1%5D = 40 km/h;
                ending  velocity  v%5B2%5D = 80 km/h;

                travel distance   d = 30 km.


To find the time, start from these two kinematic equations


    d = v%5B1%5D%2At + %28a%2At%5E2%29%2F2,      (1)

    a = %28v%5B2%5D-v%5B1%5D%29%2Ft,            (2)


where " a " is the acceleration.  Substitute (2) into (1), eliminating "a".  You will get


    d = v%5B1%5D%2At+%2B+%28%28v%5B2%5D-v%5B1%5D%29%2F%282t%29%29%2At%5E2 = v%5B1%5D%2At+%2B+%28%28v%5B2%5D-v%5B1%5D%29%2F2%29%2At = v%5B1%5D%2At+%2B+%28v%5B2%5D%2At%29%2F2+-+%28v%5B1%5D%2At%29%2F2 = %28v%5B1%5D%2At%29%2F2+%2B+%28v%5B2%5D%2At%29%2F2 = %28%28v%5B1%5D%2Bv%5B2%5D%29%2F2%29%2At.


Thus you started from the formal kinematic formula (1)  and ended with intuitively understandable formula


    d = %28%28v%5B1%5D%2Bv%5B2%5D%29%2F2%29%2At.


Now you only need substitute the given data to get simple equation


    30 = %28%2840%2B80%29%2F2%29%2At

    30 = 60t

     t = 30%2F60 = 1%2F2  of an hour = 30 minutes.    ANSWER

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


For a formal solution using basic physics, see the solution from tutor @ikleyn.

For a quick solution for this particular problem using logical reasoning, you can do the following.

(1) The acceleration is uniform from 40km/hr to 80km/hr, so the average velocity/speed is 60km/hr.

(2) 30km at an average speed of 60km/hr takes 30/60= 1/2 hour, or 30 minutes.

ANSWER: 30 minutes