# Motion Equation Problem

## Homework Statement

Sam is running at 3.8 m/s and is 75m behind John who is running at a constant velocity of 4.2m/s. If Sam accelerates at 0.15m/s^2, how long will it take him to catch John?

## Homework Equations

d = (vf+vi/2)t
vf = vi + at
d = vit + 1/2at^2
d = vft - 1/2at^2

## The Attempt at a Solution

I honestly do not know how to solve this problem...
I think I should probably find Δd of John first? His acceleration = 0, his initial and final velocity is 4.2m/s... correct? and for Sam, his initial velocity = 3.8m/s, his acceleration = 0.15m/s^s and would his Δd = -75m ....

I really don't understand this question or what I should begin to solve first and how...
Any help would be appreciated!

For Sam to catch John both of them should have the same point in space

Start by defining a distance d from the initial position of Sam to the point they will meet. Then look at the formulas.

So initial position or Δd of Sam = -75m + 3.8m/s... no?
and point they will meet is 4.2m/s + 75m? since they're both in constant motion?
I'm still really confused.

So initial position or Δd of Sam = -75m + 3.8m/s... no?
and point they will meet is 4.2m/s + 75m? since they're both in constant motion?
I'm still really confused.
Always look at your units to see if the answer makes sense!!!

The initial position of Sam can be taken as 0 and the point where they will eventually meet is a distance d from it.Now you use what you know about Sam and John plus the formulas to find two equations with the time it takes them to reach the point d .Solve them to find t.
Try drawing a diagram if you still have problems understanding.