To find the velocity of the particle when t = 2 seconds, we can use the given acceleration equation and the initial velocity.
Given: Acceleration, a = -0.2v^2 m/s^2 Initial velocity, v = 80 m/s Time, t = 2 seconds
We can solve this problem using calculus and integration, as the acceleration is a function of velocity. We'll integrate the acceleration equation with respect to time to obtain the velocity equation.
dv/dt = a dv = a dt ∫dv = ∫a dt
Integrating both sides of the equation, we get:
∫dv = ∫(-0.2v^2) dt
Integrating the left side gives us v, and integrating the right side gives us -0.2 * ∫v^2 dt.
v = -0.2 * (v^3/3) + C
To find the constant of integration, C, we can substitute the initial velocity and time:
v = -0.2 * (v^3/3) + C 80 = -0.2 * (80^3/3) + C 80 = -0.2 * (512000/3) + C 80 = -34133.333 + C C = 34213.333
Now we can substitute t = 2 seconds into the equation to find the velocity at that time:
v = -0.2 * (v^3/3) + 34213.333 v = -0.2 * (v^3/3) + 34213.333
This equation cannot be solved algebraically, so we can use numerical methods to approximate the velocity. One such method is the Newton-Raphson method. However, since the velocity equation is complex, I am unable to provide a specific numerical solution without using a numerical computing environment or calculator.