The movement of two motorcyclists is given by the equations x1 = 17 + 15t + t ^ 2 and

The movement of two motorcyclists is given by the equations x1 = 17 + 15t + t ^ 2 and x2 = 10 + 8t. Describe the type of movement of each motorcyclist, find the initial speed, acceleration, initial coordinate.

The rectilinear motion of a body in general form, having an initial coordinate x₀, is described by the equation:

x = x₀ + v₀ ∙ t + a ∙ (t ^ 2) / 2, where v₀ is the initial speed of movement, a is acceleration, t is the time of movement.

The movement of the first motorcyclist is given by the equation: x₁ = 17 + 15 ∙ t + 1 ∙ t ^ 2. Comparing its coefficients with the coefficients of the equation written in general form, we obtain:

x₀ = 17 m; v₀ = 15 m / s; a / 2 = 1 m / s ^ 2 or a = 2 m / s ^ 2.

The type of movement of the first motorcyclist is a rectilinear uniformly accelerated movement.

The movement of the second motorcyclist is given by the equation: x₂ = 10 + 8 ∙ t. Comparing its coefficients with the coefficients of the equation written in general form, we obtain:

x₀ = 10 m; v₀ = 8 m / s; a = 0 m / s ^ 2.

The movement of the second rider is straight-line uniform movement.

Answer: the straight-line uniformly accelerated motion of the first motorcyclist has an initial speed of 15 m / s, an acceleration of 2 m / s ^ 2, an initial coordinate of 17 m; the rectilinear uniform movement of the second motorcyclist has an initial speed of 8 m / s, an acceleration of 0 m / s ^ 2, an initial coordinate of 10 m.