Download and practise with this Mechanics Mathematics Subject Area Masvingo Teachers' College January 2026 question paper. Useful for university and tertiary exam revision, course practice, and preparation in Zimbabwe.
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This is the Mathematics question paper for STEP 6 Test 3 from January 2026. Use it for exam practice under timed conditions. Time allowed: 3 hours.
MASVINGO TEACHERS' COLLEGE
MATHEMATICS SUBJECT AREA
MECHANICS: YEAR 32026
STEP 6: TEST 3
3 HOURS
JANUARY 2026
INSTRUCTIONS
Answer ALL Questions
Q1. Define the following terms as there are used in mechanics angle of friction, work done, and gravitational potential energy.
[6]
Q2.a) Find the kinetic energy of a body of mass 0.003 tonnes moving with speed $4 \mathrm{~m} / \mathrm{s}$.
[3]
Q3. Find work done by the weight of a parcel of mass 5 kg falling a distance of 8 m ,
a) vertically downwards
[3]
b) down a slope inclined at $45^{\circ}$
[4]
Q3. A rough surface is inclined at an $\tan ^{-1}\left(\frac{3}{4}\right)$ to the horizontal. A body of mass 8 kg lies on the surface and is pulled at uniform speed a distance of $2,5 \mathrm{~m}$ up the plane by a force acting along a line of greatest slope. The coefficient of friction between the body and the surface is 0.025 . Find ,
a) the work done against gravity
[5]
b) the work done against friction
[5]
Q5. A particle moves along a straight line with its acceleration at any instant given by $a=\alpha+\beta v^{2}$, where $v$ is the velocity of the particle at that instant, and $\alpha$ and $\beta$ are constants. Initially the particle is at rest at a point O on the line. If the displacement of particle form O during the motion is $x$. Show that $v^{2}=\frac{\alpha}{\beta}\left(e^{2 \beta x}-1\right)$.
[6]
Q6. The magnitude of force, F , is given by $F=4+V^{2}$. Find V when $t=\frac{\pi}{2}$ seconds and $m=4 \mathrm{~kg}$. [Hint: $\int \frac{d x}{a^{2}+b^{2} x^{2}}=\frac{1}{a b} \tan ^{-1} \frac{b x}{a}+\mathrm{c}$ ]
Q7. A scud missile is projected from the ground level with a speed of $V m s^{-1}$ at an angle $\theta^{\circ}$ above the horizontal and moves freely under gravity.
a) Find an expression in terms of $V, \theta$ and $g$ for
$i$. The greatest height H , reached by the missile.
[5]
ii. Time of flight ,
[5]
iii. Range
[5]
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