CAIE IGCSE Additional Math 14.15 Use Kinematics Graphs Questions

Practise interpreting and sketching displacement, velocity, acceleration and speed graphs, alongside constant-acceleration motion calculations in Cambridge Additional Mathematics problems.

Exam points

Interpret and sketch displacement-, velocity-, acceleration- and speed-time graphs, and solve constant-acceleration motion problems.

[Maximum number: 6]

Figure for Question CAIE IGCSE Additional Math 14.15 Use Kinematics Graphs Questions question 1 — CAIE IGCSE Additional Math

The velocity-time graph represents the motion of a particle moving in a straight line.
The acceleration during the first T seconds of the motion is $2\ \mathrm{ms}^{-2}$ .
The total distance travelled is 27 m.

(a)

Calculate T.

[ 4 ]

Velocity at time T is 2T soi
$\frac{1}{2}(8+4-T)\times 2T=27$
M1 for an attempt at trapezium area or three areas and =27 using their 2T.
(T-3)(T-9)=0
M1 dep on previous M1 for solving their 3-term quadratic by factorising, completing the square, or quadratic formula.
T=3
Alternative method:
Velocity at time T is 2T, leading to $T=\frac{v}{2}$ soi
$\frac{1}{2}\left(8+4-\frac{v}{2}\right)\times v=27$
(M1) For an attempt at trapezium area =27 using their $\frac{v}{2}$ .
(18-v)(v-6)=0
(M1) Dep on previous M1 for solving their 3-term quadratic.
v=6, then T=3

(b)

Calculate the acceleration during the last 4 seconds of the motion.

[ 2 ]

$a=\frac{0-\text{their }2T}{8-4}$ oe
M1 for an attempt on gradient using their T.
-1.5
A1
Must be negative.

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CAIE IGCSE Additional Math 14.15 Use Kinematics Graphs Questions question 1

Question (a)

Question (b)