Physics, 03.07.2019 18:20 diegobebe503
The velocity of an object moving along a straight line is given by – v(t) = t 2 − 3t + 2 (a) find the displacement of the object from t = 0 to t = 3. (b) find the distance traveled from t = 0 to t = 3.
Answers: 3
![s=\int_{0}^{3}(t^2-3t+2)dt=\left [ \frac{t^3}{3}-\frac{3t^2}{2}+2t\right ]_0^3=\frac{3^3}{3}-\frac{3^3}{2}+6=1.5m](/tpl/images/0047/2913/9ece6.png)
![s=\int_{0}^{1}(t^2-3t+2)dt+\int_{1}^{2}-(t^2-3t+2)dt+\int_{2}^{3}(t^2-3t+2)dt\\\\s=\left [ \frac{t^3}{3}-\frac{3t^2}{2}+2t\right ]_0^1-\left [ \frac{t^3}{3}-\frac{3t^2}{2}+2t\right ]_1^2+\left [ \frac{t^3}{3}-\frac{3t^2}{2}+2t\right ]_2^3\\\\s=\frac{1^3}{3}-\frac{3\times 1^2}{2}+2-\left ( \frac{2^3}{3}-\frac{3\times 2^2}{2}+4\right )+\frac{1^3}{3}-\frac{3\times 1^2}{2}+2+\frac{3^3}{3}-\frac{3\times 3^2}{2}+6-\left ( \frac{2^3}{3}-\frac{3\times 2^2}{2}+4\right )=1.83m](/tpl/images/0047/2913/5ee96.png)
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The velocity of an object moving along a straight line is given by – v(t) = t 2 − 3t + 2 (a) find th...
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