The acceleration of a particle at time t t\,t seconds is a=6ti+2j m s−2\mathbf a=6t\mathbf i+2\mathbf j\text{ m s}^{-2}a=6ti+2j m s−2. Initially its velocity is (−3i+4j) m s−1(-3\mathbf i+4\mathbf j)\text{ m s}^{-1}(−3i+4j) m s−1 and its position vector is (2i−j)(2\mathbf i-\mathbf j)(2i−j) m.
Find expressions for the velocity and position vectors at time ttt.
Find the positive time at which the velocity is parallel to i+j\mathbf i+\mathbf ji+j.