A particle moves according to x = t³ − 3t² + 2t from t=0 to 2 s. Its total distance travelled is:

Question

G1 Physics · Accepted Answer

v = 3t²−6t+2. The turning times are t = 1 ± 1/√3. Write t=1+u. Then x = u³−u. At u=−1/√3: x = +2/(3√3). At u=+1/√3: x = −2/(3√3). Also x(0)=x(2)=0. Hence total distance = 2/(3√3) + 4/(3√3) + 2/(3√3) = 8/(3√3) m.