# Intersection point from acceleration [closed]

Two objects facing each other over a distance of 88m start moving from rest at an acceleration of 0.3m/s^2 and 0.2m/s^2 respectively, after how long do they intersect?

I've tried everything to find the answer and using brute force I found that they will intersect after 18.8 seconds because object a will have moved 53.016m and object b 35.344m but I don't know how to plot the problem so I don't have to use brute force.

• Can you explain your brute Force method? – Protein Sep 19 '20 at 15:14
• Show your work so far. As a hint -- do you know the equation for position vs. time given steady acceleration? – TimWescott Sep 19 '20 at 15:43
• Your 'brute force' results are certainly correct. You should show how you did that. – Gert Sep 19 '20 at 15:48
• I calculated displacement given different times for each object and kept doing that until both displacements added up to 88m and that lead me to 18.8 seconds. – Viktor Sep 19 '20 at 15:56

## 3 Answers

Could you solve the problem if one object was stationary and the second object was accelerating towards the first at $$0.5$$ m/s^2 ? Can you see how this might help you solve the original problem ?

The simplest method is to solve this problem from the frame of one of one of the particles.

Alternatively you can use the displacement equations of particles.

HINT: You need to collapse the 2 equation for the distance that is :
$$x = \frac{1}{2}at^{2}+x_{0}$$
knowing that
$$x_{firstVehicule} = x_{secondVehicule}$$
when they intersect.