Math  /  Calculus

Question41. (II) A mass mm is at rest on a horizontal frictionless surface at t=0t=0. Then a constant force F0F_{0} acts on it for a time t0t_{0}. Suddenly the force doubles to 2F02 F_{0} and remains constant until t=2t0t=2 t_{0}. Determine the total distance traveled from t=0t=0 to t=2t0t=2 t_{0}.

Studdy Solution
Sum the distances to find the total distance traveled.
stotal=s1+s2 s_{\text{total}} = s_1 + s_2 =12F0mt02+2F0mt02 = \frac{1}{2} \cdot \frac{F_0}{m} \cdot t_0^2 + 2 \cdot \frac{F_0}{m} \cdot t_0^2 =12F0mt02+42F0mt02 = \frac{1}{2} \cdot \frac{F_0}{m} \cdot t_0^2 + \frac{4}{2} \cdot \frac{F_0}{m} \cdot t_0^2 =52F0mt02 = \frac{5}{2} \cdot \frac{F_0}{m} \cdot t_0^2
The total distance traveled from t=0 t=0 to t=2t0 t=2t_0 is:
52F0mt02 \boxed{\frac{5}{2} \cdot \frac{F_0}{m} \cdot t_0^2}

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