IB Mathematics Applications & Interpretation Topic AHL 5.13—kinematic Problems Questionbank (HL)

IB Mathematics Applications & Interpretation Topic AHL 5.13—kinematic Problems Questionbank (HL) | RevisionDojo

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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Paper

Level

Question 1

HLPaper 2

The velocity of a particle, $v$ m s $^{- 1}$ , is modelled by the function $v (t) = - 3 t^{2} + 18 t - 24$ for $t \geq 0$ , where $t$ is the time in seconds.

Find the values of $t$ for which the velocity is zero.

[2]

Find $∣ v^{'} (4) ∣$ .

[3]

Find $max_{0 \leq t \leq 4} ∣ v (t) ∣$ .

[2]

Assuming the particle is at the origin at $t = 0$ , find an expression for the displacement $s$ (in metres) of the particle at time $t$ seconds.

[4]

Calculate the total distance travelled, including both forward and backward motion, in the interval $0 \leq t \leq 3$ .

[3]

Question 2

HLPaper 1

A particle moves in a plane such that its position vector (in metres) at time $t$ seconds, for $t \geq 0$ , is given by $r = (t^{2} t^{2} - 4 t)$ .

Find the velocity vector, $v$ , of the particle in terms of $t$ .

[2]

Find the position vector of the particle at the instant its speed is at a minimum.

[5]

Question 3

HLPaper 1

On a transport graph, a drone has position vector (in metres) relative to vertex $O$ at time $t$ seconds, for $0 \leq t \leq π$ , given by $r = (4 sin t 7 t + 4 cos t)$ .

Find the velocity vector, $v$ , in terms of $t$ .

[2]

Find the position vector of the drone at the instant its speed is at a minimum.

[5]

Question 4

HLPaper 1

An automated cart moves along a straight track so that, for time $t \geq 0$ , its acceleration is $a (t) = 4 t + 2$ . Its velocity is $15$ m s $^{- 1}$ when $t = 2$ s, and its displacement from the loading bay is $39$ m when $t = 3$ s.

Determine the expression for the displacement $s$ as a function of time $t$ .

[6]

Question 5

HLPaper 2

The rate of change of the volume of water in a storage tank, $R$ litres per minute, is modeled by the function $R (t) = - 3 t^{2} + 18 t - 15$ for $t \geq 0$ , where $t$ is the time in minutes.

Find the values of $t$ for which the rate of change of the volume is zero.

[2]

Find $∣ R^{'} (5) ∣$ .

[3]

Find $max_{0 \leq t \leq 5} ∣ R (t) ∣$ .

[2]

Assuming the tank is empty at $t = 0$ , find an expression for the volume of water $V$ (in litres) in the tank at time $t$ minutes.

[4]

Calculate the total volume of water transferred, including both inflow and outflow, in the interval $0 \leq t \leq 4$ .

[3]

IB Mathematics Applications & Interpretation AHL 5.13—kinematic Problems Questionbank

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IB Mathematics Applications & Interpretation AHL 5.13—kinematic Problems Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 5.13—kinematic Problems Questionbank

Unlock all 23 questions with a free account