contestada

The acceleration of a particle is given by a = c1 + c2v, where a is in millimeters per second squared, the velocity v is in millimeters per second, and c1 and c2 are constants. If the particle position and velocity at t = 0 are s0 and v0, respectively, determine expressions for the position s of the particle in terms of the velocity v and time t.

Respuesta :

onyebuchinnaji

The expression for the position of the particle in terms of velocity and time is given as, s = vt

The given expression:

  • [tex]a = c_1 + c_2v[/tex]
  • the unit of a = mm/s²
  • the velocity, v = mm/s
  • c₁ and c₂ are constant
  • the position of the particle at time, t = 0, is s₀ and v₀

To find:

  • The expression for the position s of the particle in terms of the velocity v and time t

Determine the value of the constants from second equation of motion given as:

[tex]s = vt + \frac{1}{2}at^2\\\\substitute \ the \ given \ value \ of \ a\\\\s = vt + \frac{1}{2}(c_1 + c_2v)t^2\\\\s = vt + \frac{1}{2} c_1 t^2 + \frac{1}{2} c_2vt^2\\\\divide \ through\ by \ t^2\\\\\frac{s}{t^2} = \frac{v}{t} + \frac{1}{2} c_1 + \frac{1}{2} c_2v\\\\multiply \ through \ by \ 2\\\\\frac{2s}{t^2} = \frac{2v}{t} + c_1 + c_2v\\\\when \ t = 0\\\\0 = 0 +c_1 + c_2v\\\\c_1 + c_2v = 0\\\\from \ the \ original \ equation;\\\\s = vt + \frac{1}{2} (c_1 + c_2v)t^2\\\\[/tex]

[tex]s = vt + \frac{1}{2}(0)^2\\\\s = vt[/tex]

Thus, the expression for the position of the particle in terms of velocity and time is given as, s = vt

Learn more here: https://brainly.com/question/22935373