Part of ME-02 — Kinematics

Kinematics — Visual and Tabular Summary

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Projectile Motion Diagram

v = ucosθ at peak vy = 0 H R = $u^{2}$sin2θ/g u, θ θ

Graph Interpretation Quick Reference

GraphSlopeArea
x-t (position-time)Instantaneous velocityNot directly useful
v-t (velocity-time)Instantaneous accelerationDisplacement
a-t (acceleration-time)Rate of change of accelerationChange in velocity

Complementary Angle Comparison Table

θTHR
30°u/gu/gu2/(8g)u^2/(8g)u23/(2g)0.866u2/gu^2\sqrt{3}/(2g) \approx 0.866u^2/g
45°u2/gu\sqrt{2}/gu2/(4g)u^2/(4g)u2/gu^2/g (maximum)
60°u3/gu\sqrt{3}/g3u2/(8g)3u^2/(8g)u23/(2g)0.866u2/gu^2\sqrt{3}/(2g) \approx 0.866u^2/g

Note: R30°=R60°R_{30°} = R_{60°}; H60°=3×H30°H_{60°} = 3 \times H_{30°}

Circular Motion Schematic

v (tangential) aₒ = $v^{2}$/r O r Speed constant; direction changes → acceleration exists

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