The movement of two motorcyclists is given by the equations x = 15 + t ^ 2 and x = 8t.

The movement of two motorcyclists is given by the equations x = 15 + t ^ 2 and x = 8t. Describe the movement of each motorcyclist. Determine the place and time of their meeting.

x1 (t) = 15 + t ^ 2.

x2 (t) = 8 * t.

hvs -?

tvs -?

With uniform rectilinear motion, the dependence of the coordinate of the body on time has the form: x (t) = x0 + V * t, where x0 is the initial coordinate of the body, V is the speed of uniform rectilinear motion.

x2 (t) = 8 * t – rectilinear uniform motion with a speed V1 = 8 m / s from the origin x0 = 0.

The dependence of the coordinate at uniformly accelerated motion has the form: x (t) = x0 + V0 * t + a * t ^ 2/2, where V0 is the initial speed, and is the acceleration of the motion.

x1 (t) = 15 + t ^ 2 – uniformly accelerated motion: x0 = 15 m, V0 = 0 m / s, a = 2 m / s2.

15 + t ^ 2 = 8 * t.

t ^ 2 – 8 * t + 15 = 0.

D = 64 – 4 * 15 = 4.

t = (8 ± 2) / 2.

tvs1 = 5 s, tvs2 = 3 s.

hvs1 = 40 m, hvs2 = 24 m.

Answer: tvs1 = 5 s, tvs2 = 3 s, hvs1 = 40 m, hvs2 = 24 m.