A particle P P\,P moves in a straight line through a fixed point OOO.
At time t t\,t seconds, t≥0t \geq 0t≥0, the acceleration of P P\,P is (6t−24)(6t - 24)(6t−24) m s−2^{-2}−2 measured in the positive direction.
Initially P P\,P is at O O\,O and is moving with velocity 60 m s−1^{-1}−1 in the positive direction.
Show that P P\,P never moves in the negative direction.
Find the distance travelled by P P\,P in the first 10 seconds.
265 exam-style questions on AQA A Level Maths 3.2 Q: Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Constant acceleration formulae, 3.2.4 Calculus in kinematics (A-level only), and 3.2.5 Motion under gravity and projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.