[ r(t)=(2 t+1) i+(t-4) j ] * Displacement between t_(1)=2 s and t_(2)=4 s * Average velocity between t=2 s and t=4 * velocity at t=2 s * Acceleration at t=3 mathrm(~s)

To find the displacement between and , we need to integrate the velocity function over the interval .The displacement is given by the integral of the velocity function over the given interval: Integrating the function, we get: Evaluating the integral, we have: Therefore, the displacement between and is 14 units.To find the velocity at , we simply substitute into the velocity function : Therefore, the velocity at is 5 units.To find the acceleration at , we need to take the derivative of the velocity function : Since the derivative is a constant, the acceleration at any time is 2 units.Therefore, the acceleration at is 2 units.