AHL 3.12—Vector applications to kinematics - IB Questionbank | RevisionDojo

AHL 3.12—Vector applications to kinematics Questionbank

Practice AHL 3.12—Vector applications to kinematics with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

HLPaper 1

The position of a particle is given by

\vec{r}(t)=\left[\begin{array}{c} 2 t^{2}-3 t \\ t^{3} \end{array}\right]

Find the acceleration vector ( t ) at time t .

[3]

Question 2

HLPaper 1

A particle moves such that its position at time t is given by

\vec{r}(t)=\left[\begin{array}{c} 4 t \\ 5 t+2 \end{array}\right]

Find the speed of the particle.

[2]

Question 3

HLPaper 1

Two particles A and B have position vectors:

\vec{r}_{A}(t)=\left[\begin{array}{c} 2 t+1 \\ 3 \end{array}\right], \quad \vec{r}_{B}(t)=\left[\begin{array}{c} 5-t \\ 1+2 t \end{array}\right]

Determine whether the particles ever meet.

[6]

Question 4

HLPaper 1

A particle has velocity

\vec{v}(t)=\left[\begin{array}{c} 6 \cos t \\ -6 \sin t \end{array}\right], \quad \vec{r}(0)=\left[\begin{array}{l} 0 \\ 0 \end{array}\right]

Find the position vector ( t ) and describe the path of the particle.

[6]

Question 5

HLPaper 1

A particle has position vector

\vec{r}(t)=\left[\begin{array}{l} 4 t \\ t^{2} \end{array}\right]

Show that the particle is moving on a curve and find the angle between the velocity and acceleration vectors at $\mathrm{t}=2$ .

[7]

Question 6

HLPaper 1

The velocity of a particle is given by

\vec{v}(t)=\left[\begin{array}{c} 6 t \\ -4 \end{array}\right], \quad \vec{r}(0)=\left[\begin{array}{l} 2 \\ 5 \end{array}\right]

Find the position vector ( t ) and determine the position when $\mathrm{t}=2$ .

[4]

Question 7

HLPaper 1

A particle moves with velocity vector

\vec{v}(t)=\left[\begin{array}{l} 4 \\ 2 \end{array}\right]

starting from the origin.

How far is the particle from the origin after 3 seconds?

[4]

Question 8

HLPaper 1

A particle's velocity is given by

\vec{v}(t)=\left[\begin{array}{c} 2 t \\ 3 \end{array}\right], \quad \vec{r}(0)=\left[\begin{array}{l} 0 \\ 1 \end{array}\right]

At what time will the particle be 5 units above the x-axis?

[3]

Question 9

HLPaper 1

A particle has position vector

\vec{r}(t)=\left[\begin{array}{c} 6-2 t \\ 4 t \end{array}\right]

Find the time when the particle is at the origin.

[3]

Question 10

HLPaper 1

A particle moves such that its position at time t seconds is given by

\vec{r}(t)=\left[\begin{array}{c} 4 t^{2}+1 \\ 2 t-3 \end{array}\right]

Determine the time(s), if any, when the particle is moving vertically.

[5]

Paper

Level

Question 1

HLPaper 1

The position of a particle is given by

\vec{r}(t)=\left[\begin{array}{c} 2 t^{2}-3 t \\ t^{3} \end{array}\right]

Find the acceleration vector ( t ) at time t .

[3]

Question 2

HLPaper 1

A particle moves such that its position at time t is given by

\vec{r}(t)=\left[\begin{array}{c} 4 t \\ 5 t+2 \end{array}\right]

Find the speed of the particle.

[2]

Question 3

HLPaper 1

Two particles A and B have position vectors:

\vec{r}_{A}(t)=\left[\begin{array}{c} 2 t+1 \\ 3 \end{array}\right], \quad \vec{r}_{B}(t)=\left[\begin{array}{c} 5-t \\ 1+2 t \end{array}\right]

Determine whether the particles ever meet.

[6]

Question 4

HLPaper 1

A particle has velocity

\vec{v}(t)=\left[\begin{array}{c} 6 \cos t \\ -6 \sin t \end{array}\right], \quad \vec{r}(0)=\left[\begin{array}{l} 0 \\ 0 \end{array}\right]

Find the position vector ( t ) and describe the path of the particle.

[6]

Question 5

HLPaper 1

A particle has position vector

\vec{r}(t)=\left[\begin{array}{l} 4 t \\ t^{2} \end{array}\right]

Show that the particle is moving on a curve and find the angle between the velocity and acceleration vectors at $\mathrm{t}=2$ .

[7]

Question 6

HLPaper 1

The velocity of a particle is given by

\vec{v}(t)=\left[\begin{array}{c} 6 t \\ -4 \end{array}\right], \quad \vec{r}(0)=\left[\begin{array}{l} 2 \\ 5 \end{array}\right]

Find the position vector ( t ) and determine the position when $\mathrm{t}=2$ .

[4]

Question 7

HLPaper 1

A particle moves with velocity vector

\vec{v}(t)=\left[\begin{array}{l} 4 \\ 2 \end{array}\right]

starting from the origin.

How far is the particle from the origin after 3 seconds?

[4]

Question 8

HLPaper 1

A particle's velocity is given by

\vec{v}(t)=\left[\begin{array}{c} 2 t \\ 3 \end{array}\right], \quad \vec{r}(0)=\left[\begin{array}{l} 0 \\ 1 \end{array}\right]

At what time will the particle be 5 units above the x-axis?

[3]

Question 9

HLPaper 1

A particle has position vector

\vec{r}(t)=\left[\begin{array}{c} 6-2 t \\ 4 t \end{array}\right]

Find the time when the particle is at the origin.

[3]

Question 10

HLPaper 1

A particle moves such that its position at time t seconds is given by

\vec{r}(t)=\left[\begin{array}{c} 4 t^{2}+1 \\ 2 t-3 \end{array}\right]

Determine the time(s), if any, when the particle is moving vertically.

[5]