time/speed graph [Solved!]

X

In the following time/speed graph, the horizontal line shows the time taken by a car and the vertical axis shows the speed (u cms/sec).

if D is the distance travelled from the start for 20 seconds, find t for 2D.

<img src="/forum/uploads/imf-0544-kinetics2.jpg" width="500" height="246" alt="series-binomial-theorem" />

Relevant page

<a href="/kinematics/1-velocity-graphs.php">1. Velocity (s-t) Graphs</a>

What I've done so far

Please confirm that the answer is correct.

workings: D = 1/2 x u x 20
            = 10u
         2D = 10u x 2
            = 20u
     TTaken = 20u/u
            =20 secs

X

Swalay

You are encouraged to use the <a href="http://www.intmath.com/forum/entering-math-graphs-images-41/how-to-enter-math:91">Math entry system</a> for this forum so your math is nicely aligned, and looks like mathematics.

For example your first line would look like: `D = 1/2 xx u xx 20`

Your first 4 lines are correct.

Suggestions:

(1) It's OK to introduce your own variables, but make sure you answer what the question asks for (which is `t` in this case).

(2) Think about the big picture first. If it took the car 20 seconds to travel `D` cm (while accelerating from rest), will it take another 20 s to travel the same distance?

X

No.  It will take lesser time according to me.
If speed is not constant and acceleration is not zero, less time is needed to cover the same distance after acceleration = 0

X

Correct - but your answer says (I think) that the 2nd part of the journey takes 20 seconds (which is the same as the first part), so there is an inconsistency.

<b>Hint:</b> to see what's going on, you could try a reasonable numerical value for u (say 1000, which is equivalent to about 38 km/h). Often it's easier to work with numbers than algebra.

X

If 2D = 20u this is the total distance travelled for the first part of the question.

Time taken for the first D = 20 secs (its includes acceleration)
Time taken for the second D < 20 secs (there is no acceleration)but now I cannot proceed.

X

I can't see where you have tried what I suggested.

Often we can't see what's going on when just using algebra. Try a real number for `u` (1000, say) first to get a sense of the situation.

This is what I mean:

First part of the journey (first 20 seconds):

`D=10u=10,000 "cm"`

Now, the second part of the journey also needs to be `D=10,000 "cm"` long. But we are now going at `u=1000 "cm/s"`, so how many seconds will that second part take?

X

Time taken is Distance divided by speed
where D = 10,000 and speed is U = 1000cm/s
So that time taken = 10 secs

Therefore time taken from the start (that is from t = 0) is 20secs + 10 secs= 30 secs

X

The second part of the answer as to when the car will stop, this I know.

Please confirm the result so far.

X

Yes, your answer is correct for our "pretend" value of `u`.

Now you just need to express it algebraically, using `u` only.

X

Thank you very much for your patience with me in this question.

X

You're welcome.

But I can't see that you have completed the question (using `u`).

I meant something like this:

<b>Journey part 1</b>

Distance travelled `= D = 1/2 xx u xx 20 = 10u`

Time taken `= 20"s"`

<b>Journey part 2</b>

Distance travelled `=D=10u`

Time taken `=(10u)/u = 10 "s"`

So `t = 20 + 10 = 30 "s"`.

Always directly address the given question, using the original variables!