## Homework Statement

In a long distance race, Michael is running at 3.8 m/s and is 75 m behind Robert, who is running at a constant velocity of 4.2 m/s. If Michael accelerates at 0.15 m/s^2, how long will it take him to catch Robert

## Homework Equations

D=vi(delta)t + 1/2a(delta)t^2
etc

## The Attempt at a Solution

I know how to do this type of problem when the accelerating runner starts from a rest, but I have no idea where to go from here. I've tried framing the problem a bunch of different ways but nothing.

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tiny-tim
Homework Helper
welcome to pf!

hi bcaie16! welcome to pf! (have a delta: ∆ and try using the X2 and X2 icons just above the Reply box )

you need to write two separate equations, one for each runner …

what do you get? Delphi51
Homework Helper
Welcome to PF, bcaie16! Nice to see some high school work here.
The thing that determines the answer is that the two people meet - their distances become equal. So you should begin with
Michael's distance = Robert's distance

Robert's distance is easy - just use d = vt and add 75 because he is starting out that far ahead.

Michael's distance is complicated because of the initial velocity and acceleration. Use the standard distance formula for accelerated motion: d = Vi*t + .5*a*t².

It looks like you will have a quadratic equation to solve. If you are just starting grade 11 math you may need to look up how to solve a quadratic on a calculator or using the general formula:

You can, of course, solve it by trial and error. A spreadsheet works really well for that.

I figured I would have to use the quadratic formula. I wasn't sure how to frame it kinematics wise. What are the a, b, and c values respectively in terms of velocity, acceleration, etc.

Ok i figured that the respective equations would be ∆t= 4.2 ∆D +75, and
75= -∆t +/- square root ∆t -2.28/2

tiny-tim
Homework Helper
Ok i figured that the respective equations would be ∆t= 4.2 ∆D +75, and
75= -∆t +/- square root ∆t -2.28/2
nooo (btw, why are you using all these ∆s? it's not normal, and it really doesn't help)

∆t= 4.2 ∆D +75 is completely wrong, isn't it?

and i can't work out what your second equation is just write two general equations, one for each runner (ignoring the other) …

when you have them, then you can decide how to use them​

Ok being completely new to physics, I am kind of lost. I am not really sure to how to get a general equation. Should they be in relation to time or distance

tiny-tim
Homework Helper
both …

each should be x = a function of t

(ie it tells you where it is at each time t )

Delphi51
Homework Helper
Michael's distance = Robert's distance
vt + .5*a*t² = vt + 75
3.8*t + .5*(.15)*t² = 4.25 + 75
collect like terms, all on one side, so you have an equation of the form
at² + bt + c = 0
Then use one of the methods of solving the quadratic for t.

Delphi51
Homework Helper
Oops, forgot a t in the previous post. Too late to edit. Should be like this:
Michael's distance = Robert's distance
vt + .5*a*t² = vt + 75
3.8*t + .5*(.15)*t² = 4.2t + 75
collect like terms, all on one side, so you have an equation of the form
at² + bt + c = 0
Then use one of the methods of solving the quadratic for t.