As the signal turns green, automobile A accelerates at a constant rate of 2 m/s2. Two seconds later, automobile B starts and accelerates at a constant rate of 3.6 m/s2. Determine (a) when B will overtake A, (b) the speed of each automobile at that time, and c) the location where B overtakes A relative to the traffic signal.

a) 45 s , b)    vₐ = 90 m / s, v_b = 162 m / s, c)     x_b = 3.328 10⁴ m

Explanation:

We can solve this exercise using the kinematic relations

Vehicle A

              xₐ = v₀ₐ t + ½ aₐ t²

vehicle B

starts two seconds later

             x_b = v_{ob} (t-2) + ½  a_b (t-2) ²

as cars start from rest their initial velocities are zero

at the point where they meet, the position must be the same for both vehicles

             xa = 0 + ½ aₐ t²

             xb = 0 + ½ a_b (t-2) ²

             ½ aₐ t² = ½ a_b (t-2) ²

            t = (t-2)

              t (1 - \sqrt{  \frac{a_a}{a_b} }) = 2

             t (1 - ⅔, ) = 2

            t = 2 / 0.4444

             t = 45 s

b)

the speed of each car

                vₐ = voa + aa t

                vₐ = 0 + 2 45

                vₐ = 90 m / s

                v_b = 3.6 45

                v_b = 162 m / s

c) xb = 0 + ½ ab (t-2) ²

       x_b = ½ 3.6 (45-2) ²

       x_b = 3.328 10⁴ m

the skeletons of most mammals reach a certain size and then stop growing. however, many animals, including some mammals, keep growing throughout their lives. kangaroos, for example, just keep growing and growing until they die. also, the longer an animal lives the greater the chance it might catch some deadly disease.