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MHT-CET Physics · Formula sheet

Motion in a Plane formulas

7 formulas and 12 common traps for MHT-CET Physics Motion in a Plane, grouped by subtopic.

Full notes with worked examples

Vectors: Addition and Products

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Adding Vectors

Resultant

R2=A2+B2+2ABcos⁡θR^2 = A^2 + B^2 + 2AB\cos\theta

Dot and Cross Products

Products

A⃗⋅B⃗=ABcos⁡θ,∣A⃗×B⃗∣=ABsin⁡θ\vec{A}\cdot\vec{B} = AB\cos\theta, \qquad |\vec{A}\times\vec{B}| = AB\sin\theta

Common traps

Any three vectors form a triangle

Only if they close. Check whether one is the sum of the other two; if not, they form no triangle whatever their lengths.

Using sin for the dot product

Dot uses cos θ, cross uses sin θ. At 30°, AB sin θ is half of AB; AB cos θ is (√3/2)AB.

Expecting a cross product to lie in the plane of its vectors

A × B is perpendicular to both A and B, so any sum of A, B and their multiples is perpendicular to it — the angle is 90°, whatever the numbers.

Equations of Motion and Motion Graphs

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The Equations of Motion

Equations of motion

v=u+at,s=ut+12at2,v2=u2+2asv = u + at, \qquad s = ut + \tfrac{1}{2}at^2, \qquad v^2 = u^2 + 2as

Motion Graphs and Calculus

Calculus of motion

v=dxdt,a=dvdt,Δx=∫v dtv = \frac{dx}{dt}, \qquad a = \frac{dv}{dt}, \qquad \Delta x = \int v\,dt

Common traps

Averaging speeds over equal distances

Equal DISTANCES take unequal times, so the average speed is the harmonic mean. V and V/3 give V/2, not 2V/3.

Running the equations past the stop

A vehicle braking from 15 m/s at 0.3 m/s² stops at 50 s. After that it stays put; s = ut + ½at² at 60 s would have it reversing.

Using s = ½at² when a changes with time

With a = 6t + 5, the equations of motion do not apply. Integrate a to get v, then v to get x.

Relative Motion and Meeting Problems

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Relative Velocity and Meeting

Relative velocity

v⃗AB=v⃗A−v⃗B\vec{v}_{AB} = \vec{v}_A - \vec{v}_B

Common traps

Using the sum of speeds for trains going the same way

Same direction: the faster gains only by the DIFFERENCE of speeds. Opposite directions: the sum.

Forgetting both train lengths

Crossing is complete when the rear of one passes the rear of the other: the distance is the sum of the two lengths.

Projectiles

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Time of Flight, Height and Range

Projectile

T=2usin⁡θg,H=u2sin⁡2θ2g,R=u2sin⁡2θgT = \frac{2u\sin\theta}{g}, \qquad H = \frac{u^2\sin^2\theta}{2g}, \qquad R = \frac{u^2\sin 2\theta}{g}

Common traps

Using cos θ for the vertical motion

The vertical component is u sin θ; the horizontal is u cos θ. Time of flight and height come from sin θ.

Assuming a throw from a tower goes upward

'At 30° with the horizontal' does not say which side. A throw 30° below lands 8.7 m out from a 10 m tower at 10 m/s; 30° above lands 17.3 m out.

Uniform Circular Motion

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Centripetal Acceleration, Banking and the Vertical Circle

Centripetal acceleration

a=v2r=ω2r,tan⁡θ=v2rga = \frac{v^2}{r} = \omega^2 r, \qquad \tan\theta = \frac{v^2}{rg}

Common traps

Calling the acceleration constant

Its magnitude v²/r is constant but its direction turns with the body. Only the kinetic energy and speed are truly constant.

Confusing instantaneous and average acceleration

Over half a circle the average acceleration is 2v²/(πr), smaller than the instantaneous v²/r.

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