A particle moves in a straight line. Its acceleration a m s−2a\text{ m s}^{-2}a m s−2 is modelled by a=4t−t2a=4t-t^2a=4t−t2 for 0≤t≤30\leq t\leq30≤t≤3, and by a=−3a=-3a=−3 for 3<t≤63<t\leq63<t≤6. The particle starts from rest at the origin. The velocity is continuous at t=3t=3t=3.
Find the velocity for 0≤t≤30\leq t\leq30≤t≤3.
Find the velocity for 3<t≤63<t\leq63<t≤6.
Find the total distance travelled in the first 6 seconds.
204 exam-style questions on CCEA A Level Maths 4.1 Kinematics (A-level only), covering 4.1.1 Kinematics (A-level only), 4.1.2 Kinematics (A-level only), and 4.1.3 Kinematics (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.