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IB Physics · Theme A · A.1

Kinematics,
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Key Notes

Read the approved A.1 Kinematics Key Notes.

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A.1 Kinematics — Complete Key Notes

Complete IB DP Physics A.1 revision notes covering one- and two-dimensional motion, motion graphs, SUVAT, projectile motion, uniform circular motion and relative motion.

A.1 Kinematics — Complete Key Notes

Motion quantities

•Distance is total path length; displacement is directed position change.
•Speed is the rate of change of distance; velocity is v⃗=ds⃗/dt\vec v=d\vec s/dt.
•Acceleration is a⃗=dv⃗/dt\vec a=d\vec v/dt and can change speed, direction, or both.

Motion graphs

•Displacement–time gradient gives velocity.
•Velocity–time gradient gives acceleration; signed area gives displacement.
•Acceleration–time signed area gives change in velocity.

Constant acceleration

Use only when acceleration is uniform:

v=u+atv=u+at
s=ut+12at2s=ut+\frac12at^2
s=u+v2ts=\frac{u+v}{2}t
v2=u2+2asv^2=u^2+2as

Motion in a plane

Resolve vectors into perpendicular components:

vx=vcos⁡θ,vy=vsin⁡θv_x=v\cos\theta,\qquad v_y=v\sin\theta

Treat components independently but use the same time coordinate.

Projectile motion

With air resistance neglected and upward positive:

x=uxtx=u_x t
y=uyt−12gt2y=u_y t-\frac12gt^2
vy=uy−gtv_y=u_y-gt
•Horizontal acceleration is zero.
•Vertical acceleration is −g-g.
•At maximum height vy=0v_y=0, but acceleration remains downward.
•For launch and landing at the same height: T=2usin⁡θ/gT=2u\sin\theta/g and R=u2sin⁡2θ/gR=u^2\sin2\theta/g.

Uniform circular motion

Speed may be constant while velocity changes direction.

ω=2πT=2πf\omega=\frac{2\pi}{T}=2\pi f
v=ωrv=\omega r
ac=v2r=ω2ra_c=\frac{v^2}{r}=\omega^2r

Centripetal acceleration points toward the circle's centre; it is produced by the resultant inward force, not by an additional force called “centripetal force”.

Relative motion

v⃗A/B=v⃗A−v⃗B\vec v_{A/B}=\vec v_A-\vec v_B

Use component subtraction for two-dimensional relative velocity.

Exam checklist

•State a positive direction before using signed quantities.
•Do not use SUVAT when acceleration changes.
•Separate horizontal and vertical projectile equations.
•In circular motion, distinguish constant speed from constant velocity.
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