Question

In the figure here, a red car and a green car move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at xr = 0 and the green car is at xg = 221 m. If the red car has a constant velocity of 25.0 km/h, the cars pass each other at x = 44.1 m. On the other hand, if the red car has a constant velocity of 50.0 km/h, they pass each other at x = 76.2 m. What are (a) the initial velocity and (b) the (constant) acceleration of the green car? Include the signs.

answers to 4 sig figs

Answer 1

Vr = 25km/h * 1m/s / 3.6km/h = 6.94 m/s:

Sr =44.1 m = 6.94m/s * t

→ this tells us t = 44.1/6.94 s = 6.35s

Sg = 44.1 m = 221m + Vg * t + ½at²

Plug in for t:

44.1 = 221 + 6.35Vg + 20.16a

-6.35Vg = 176.9 + 20.16a

Vg = -27.86 - 3.17a ← for later

Vr = 50km/h * 1m/s / 3.6km/h = 13.89 m/s:

Sr = 76.2m = 13.89m/s * t

→ t = 5.49 s

Sg = 76.2m = 221m + Vg * t + ½at²

Sub for t and Vg:

76.2 = 221 + (-27.86 - 3.17a)(5.49) + ½a(5.49)²

76.2 = 221 - 152.95 - 17.4a + 15.04a

8.15 = -2.3633 a

(part b) a = -3.449 m/s² ← acceleration

(a) Thus, Vg = -27.86 - 3.17(-3.45) = -16.93 m/s ← initial velocity