To find the distance moved by the particle, we need to integrate the velocity function with respect to time over the desired interval.
Given that the velocity function is v(t) = -2t + 4 m/s, we integrate it to find the displacement function:
s(t) = ∫v(t) dt
Integrating the velocity function, we get:
s(t) = ∫(-2t + 4) dt = -t^2 + 4t + C
Here, C is the constant of integration.
To find the distance moved, we need to evaluate the displacement function between two time points, t1 and t2, and take the absolute value of the result:
Distance = |s(t2) - s(t1)|
Let's assume t1 = 0 and find the distance moved up to a time t2:
Distance = |s(t2) - s(0)| = |(-t2^2 + 4t2) - (-(0)^2 + 4(0))| = |(-t2^2 + 4t2) - 0| = |(-t2^2 + 4t2)|
So, the distance moved by the particle is |(-t2^2 + 4t2)| units.