Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 5.13—kinematic Problems with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 5.13—kinematic Problems and mirrors Paper 1, 2, 3 style where relevant.
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The velocity of a particle, m s, is modelled by the function for , where is the time in seconds.
(a) Find the values of for which the velocity is zero.
(b) Find .
(d) Assuming the particle is at the origin at , find an expression for the displacement (in metres) of the particle at time seconds.
A particle moves in a plane such that its position vector (in metres) at time seconds, for , is given by .
(a) Find the velocity vector, , of the particle in terms of .
(b) Find the position vector of the particle at the instant its speed is at a minimum.
On a transport graph, a drone has position vector (in metres) relative to vertex at time seconds, for , given by .
(a) Find the velocity vector, , in terms of .
(b) Find the position vector of the drone at the instant its speed is at a minimum.
An automated cart moves along a straight track so that, for time , its acceleration is . Its velocity is m s when s, and its displacement from the loading bay is m when s.
A particle moves in a plane such that its position vector (in metres) at time seconds, for , is given by .
(a) Find the velocity vector, , of the particle in terms of .
(b) Find the position vector of the particle at the instant its speed is at a minimum.
(e) the total distance travelled, including both forward and backward motion, in the interval .
the expression for the displacement as a function of time .
