Physics equations/03-Two-Dimensional Kinematics/A:2DmotionHint

Calculating the time when two particles meet

If two particles have different accelerations and initial conditions, and we want to know where they meet, it is best to first ask when they meet. Also, with two particles, we either need subscripts or primes to distinguish them. When doing a physics problem, take some time to select appropriate labels. Consider the following two options:

Subscript option:

$x_b=x_{b0}+v_{b0}t+\frac{1}{2}{a}_b{t}^2$

$x_c=x_{c0}+v_{c0}t+\frac{1}{2}{a}_c{t}^2$

Here we avoided the "a" subscript since "a" already means accelerations. To avoid a "subscript orgy" we can use primes:

$x=x_0+v_{0}t+\frac{1}{2}a{t}^2$

$x^{\prime }=x_{0^{\prime }}+v_{c^{\prime }}t+\frac{1}{2}{a}^{\prime }{t}^2$

Equation $x_b=x_c$, we have:

$x_0+v_{0}t+\frac{1}{2}a{t}^2=x_{0^{\prime }}+v_{0^{\prime }}t+\frac{1}{2}{a}^{\prime }{t}^2$

Before solving for time, we first ascertain why kind of equation this is. It is quadratic in the unknown, and therefore requires a quadratic equation.