The equations of motion for trucks and cars have the form, respectively, x1 = 600–10t and

The equations of motion for trucks and cars have the form, respectively, x1 = 600–10t and x2 = t ^ 2. Determine the time of their meeting.

Given:

x1 (t) = 600 – 10 * t – the equation of motion of the truck;

x2 (t) = t ^ 2 – the equation of motion of a passenger car.

It is required to determine t (second) – the time of meeting of two cars.

When cars and trucks meet, their coordinates will be equal. I.e:

x1 = x2;

600 – 10 * t = t ^ 2.

We get a quadratic equation:

t ^ 2 + 10 * t – 600 = 0.

We find the discriminant:

D = 10 ^ 2 + 4 * 600 = 100 + 2400 = 2500.

D ^ 0.5 = 2500 ^ 0.5 = 50.

The roots of the quadratic equation will be:

t1 = (-10 + 50) / 2 = 40/2 = 20 seconds.

t2 = (-10 – 50) / 2 = -60 / 2 = -30 seconds (does not match the condition of the problem).

Answer: cars will meet in 20 seconds after the start of movement.