Average velocity, as I have heard, cannot be found simply by finding the average of two numbers. I have a question on average velocity, but am simply unable to proceed:

A particle moving in a straight line covers half the distance with speed of 3m/s. The other half of the distance is covered in two equal time intervals with speed 4.5m/s and 7.5m/s respectively. The average speed of the particle during this motion is?

What I know: The average speed is the total distance divided by the total time How exactly should I approach the question?

  • $\begingroup$ Have you tried finding the total distance and dividing by the total time? $\endgroup$ – Jordan Jun 13 '14 at 18:59
  • $\begingroup$ Can't find the distance :( $\endgroup$ – Gummy bears Jun 13 '14 at 19:00
  • $\begingroup$ you don't have to assume it any arbitrary variable $\endgroup$ – DSinghvi Jun 13 '14 at 19:05

v1=3, v2=4.5 , v3=7.5

let total distance be s

so average speed =total distance/total time.

total distance =s

time for 1st half distance = s/2/v1

for second half distance covered = s/2 =distance covered in 2 equal time intervals (say time interval be t)=t*4.5+t*7.5=t(4.5+7.5)=t(12)

so here t={s/2}/12

average speed={s}/[{s/2}/3+s/24+s/24]=s/{6s/24}=4m/s since 2t was time for second journey

  • $\begingroup$ I think that's wrong, the answer is supposed to be 4 m/s $\endgroup$ – Gummy bears Jun 13 '14 at 19:08
  • $\begingroup$ "total distance =s time for 1st half distance = s/v1" seems like typo, you need to divide s by 2. $\endgroup$ – DavePhD Jun 13 '14 at 19:10
  • $\begingroup$ you are right @Gummybears $\endgroup$ – DSinghvi Jun 13 '14 at 19:16
  • $\begingroup$ Yeah, but that's cause I have the answer key. I don't get how to reach that answer. Using his method, I too reached the same answer :( $\endgroup$ – Gummy bears Jun 13 '14 at 19:18
  • $\begingroup$ I have edited see.@Gummybears $\endgroup$ – DSinghvi Jun 13 '14 at 19:19

Hint: Pick a distance. It doesn't matter, it will divide out. $45$ meters is handy. Now calculat the total time required from the information given. We know the first $22.5$ m was covered at $3$ m/sec, so how many seconds were required? How many seconds are required for the other two pieces? Now divide your distance by the total time.


You can average the speeds in the second half, since they are for equal time intervals.

Let the total distance be a variable (d).

Solve for the time for each half segment, in terms of d.

Add the times together to get the total time.

Apply the definition you mention: "average speed is the total distance divided by the total time".

  • $\begingroup$ But for the second half, they are divided in terms of time! Please help! $\endgroup$ – Gummy bears Jun 13 '14 at 19:10
  • $\begingroup$ I edited to explain more. $\endgroup$ – DavePhD Jun 13 '14 at 19:19

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