Final answer:
The total distance covered by the particle between t=0 and t=5 is determined by calculating the integral of the absolute value of the derivative of the position function, which in this case equals 60 units.
Step-by-step explanation:
The position of a particle is governed by the given equation x(t)=3t2−2t+5. To find the total distance covered by the particle, however, we need to compute the particle's velocity by taking the derivative of the position function with respect to time.
The derivative of x(t) = 3t2−2t+5 is dx/dt = 6t-2. We need to calculate the integral of the absolute value of the velocity from t=0 to t=5. This is to account for any changes in the direction of the particle (as it can travel back and forth, the integral of the absolute value of its velocity will provide the total path length covered).
In this case, dx/dt is always positive between t=0 to t=5. So, the total distance covered by the particle is the integral from 0 to 5 of (6t-2) dt, which is [3t2 - 2t] evaluated between 0 and 5. This yields (3*52 - 2*5) - (3*02 - 2*0)= 60 units.
Learn more about Particle Motion