IB Maths AA SL 5.9 Kinematics Questions

Practise identifying the mathematical structure in a kinematics problem, selecting the correct theorem or algorithm, and checking the result with units, graphs or logical reasoning.

Exam points

Use s, v and a with v = ds/dt and a = dv/dt = d²s/dt² to relate displacement, velocity and acceleration in one-dimensional motion.
Integrate velocity to find displacement and integrate speed |v(t)| to find total distance, splitting the interval when the velocity changes sign.

[Maximum number: 4]

The velocity of a particle in $\mathrm{ms}^{-1}$ is given by $v=\mathrm{e}^{\sin t}-1$ , for $0 \leq t \leq 5$ .

Find the total distance travelled by the particle in the first five seconds.

recognizing distance is area under velocity curve
valid approach to find the total area
$e g \quad$ area A+ area $\mathrm{B}, \int v \mathrm{~d} t-\int v \mathrm{~d} t, \int_{0}^{3.14} v \mathrm{~d} t+\int_{3.14}^{5} v \mathrm{~d} t, \int|v|$
correct working with integration and limits (accept d x or missing d t )
eg $\quad \int_{0}^{3.14} v \mathrm{~d} t+\int_{5}^{3.14} v \mathrm{~d} t, 3.067 \ldots+0.878 \ldots, \int_{0}^{5}\left|\mathrm{e}^{\sin t}-1\right|$
distance $=3.95(\mathrm{~m})$

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IB Maths AA SL 5.9 Kinematics Questions question 1