Question

A student sees a Campus Bus at a stop ahead and sprints at a top speed of 6.o m/s to catch up with it. When he is 20 meters away, the driver pulls away at 1.o m/s2. Will the student catch the bus? If so, how many seconds after the bus begins to move? How far wil the bus have moved? If not, how close will the student get? How long after the bus started to move is he the closest?

Answer 1

Lets forget for a moment when (time) the student starts catching the bus . Also forget his initial position from where he starts.

For a simplicity let's have a close look at the figure attached above:

Let's choose a reference line from where our observation and calculation will start.

And this reference position is O

From reference line, distance B/w student and bus is 20 m

And the same is reprensted by OA

Let t be the time from reference position

• S1 is the Distance covered by student in t time
• X is the Distance covered by bus in t time.
• S2 is the Distance of bus from reference line

Lets check its root . Real root will say their meeting time

and imaginary root will not say anything about their time .

2 2 theu meetm They will herer meet ere Now to murmust austane(s) we hare to differentiate' eretr

Now minimisinng their difference of distance.

Differentiate (s) w.r.t time

Calculating their closest distance.

Calculating last part of question