Question

Two particles, A and B, are moving in a straight line. Take this to be the x-axis. At t = 0, particle A is trailing particle B, initially at some distance x behind B. Particle B is accelerating at a constant 2.00 m/s2 and particle A is constantly accelerating at 3.00 m/s2. Particle A was able to overtake B after B has moved 50.0 m

(a)How long does it take for particle A to overtake B?

(b)Initially, how far was A behind B?

(c)How fast are the two particles moving as soon as they’re at the same position?

Answer 1

(a) The time required for B to cover 50 m (and, thus, for A to overtake B)

$$t=\sqrt{\frac{2d}{a_B}}=\sqrt{\frac{2(50)}{2}}=7.07\text{ s}.$$

(b) The distance can be found from the following condition:

$$t=\sqrt{\frac{2(d+x)}{a_A}},\\\space\\ x=\frac{a_At^2}{2}-d=\frac{3\cdot7.07}{2}-50=25\text{ m}.$$

(c) Calculate their velocities:

$$v_B=a_Bt=14.1\text{ m/s},\\ v_A=a_At=21.2\text{ m/s}.$$