Intersection point of two moving objects

Question

Suppose we have 2 moving objects along a linear path:

The first object moves at 5 metres/second.

The second object accelerates at 1.5 metres/second.

How would one calculate the point (in time) where both objects have the same position?

Answer 1

Distance traveled with constant acceleration is given by $$ d = v_i t + \frac{1}{2} a t^2 $$ where you have $v_i=0$ for the accelerating object. The distance traveled at constant velocity is $$ d = vt $$ So you are looking for $t$ such that $$ \frac{1}{2}(1.5) t^2 = (5)t $$