Consider a rabbit that is at x=8.1m at t=0s and moves with a constant velocity of -1.6 m/s. What is the equation of motion for the rabbit?

Answer 1

Given:

Xo = 8.1 m @ t = 0 seconds

V = -1.6 m/s (constant velocity)

Solution

Start with the definition of velocity

V = dx/dt

Separate variable

Vdt = dx

Integrate both sides

Velocity is constant so we can pull it out of the integral

V ∫dt = ∫dx

Apply boundary conditions

V (t-0) = X - Xo

X = Vt + Xo

X = -1.6t + 8.1 (units: m)

Answer 2

Well at time 0, x=8.1, and moves -1.6 m/s, so

x = 8.1 - 1.6 t

t = time in seconds