Question

A particle moves in a straight line and its speed depends on time as $v=|2t-3|$. Find the displacement of the particle in $5s$.

Answer 1

$V={\int }_{(+2t-3)3\le t}^{-(2t-3)0\le t<\frac{3}{2}}=\int vdt=-{\int }_0^{\frac{3}{2}}(2t-3)dt+{\int }_{\frac{3}{2}}^5(+2t-3)dt=-{[t^2-3t]}_0^{\frac{3}{2}}+{[+t^2-3t]}_{\frac{3}{2}}^5=-\frac{9}{4}+\frac{9}{2}+25-15-\frac{9}{4}+\frac{9}{2}=10+\frac{9}{2}=\frac{29}{2}$