A particle P P\,P moves with constant acceleration 3i−4j ms−23\mathbf{i} - 4\mathbf{j} \text{ ms}^{-2}3i−4j ms−2. When t=0t = 0t=0, the particle is at the origin, OOO, and moving with a velocity 2i−3j ms−12\mathbf{i} - 3\mathbf{j} \text{ ms}^{-1}2i−3j ms−1
Find the velocity of P P\,P at time t=5t = 5t=5
Show that the position vector of P P\,P at time t t\,t is (32t2+2t)i+(−2t2−3t)j\displaystyle \left(\frac{3}{2}t^2 + 2t\right)\mathbf{i} + (-2t^2 - 3t)\mathbf{j}(23t2+2t)i+(−2t2−3t)j
At time t=Tt = Tt=T seconds, where T>0T > 0T>0, P P\,P passes through the point AAA. The position vector of A A\,A is ki−10j mk\mathbf{i} - 10\mathbf{j} \text{ m}ki−10j m relative to OOO, where k k\,k is a constant. Find the value of TTT.
Hence, find the value of kkk.
363 exam-style questions on Edexcel A Level Maths Further Kinematics, covering 8.1 Vectors in Kinematics, 8.2 Vector Methods with Projectiles, 8.3 Variable Acceleration in One Dimension, 8.4 Differentiating Vectors, and 8.5 Integrating Vectors. Each one has a worked solution and a mark scheme showing where the marks go.