Determining Velocity and Jerk from a Rational Acceleration Function
A particle moves along a straight line and its acceleration is given by \(a(t)= \frac{6t+2}{t^2+t-2}\) for values of \(t\) such that \(t^2+t-2 \neq 0\). (i) Given that the initial velocity is \(v(0)= 4\,m/s\), determine the velocity function \(v(t)\) by integrating the acceleration. Use partial fractions to express the integral in a simplified form. (ii) Find […]