Let a (T), V (T), and R (T) Denote the Acceleration

Essay

Let a (t), v (t), and r (t) denote the acceleration, velocity, and position at time t of an object moving in the xy-plane. Find r (t), given that $\mathbf { a } ( t ) = \left\langle e ^ { 2 t } + 2 t , e ^ { 2 t } - 3 \right\rangle \mathbf { v } ( 0 ) = \left( \frac { 3 } { 2 } , \frac { 7 } { 2 } \right) \text { and } \mathbf { r } ( 0 ) = \left( \frac { 5 } { 4 } , \frac { 9 } { 4 } \right)$