Vector Important Graphs _ One-Shot Revision Sheet for NEET Physics

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Visualize Understand VECTOR IMPORTANT GRAPHS Remember ONE-SHOT REVISION SHEET Quick Reminders BASIC VECTOR REPRESENTATIONS Vector quantity with both magnitude and direction. Column Vector Position Vector Vector in 2D Scalars magnitude only. Ax A A = F P(x,y,z) Graphs help us understand the relation between Ay vectors and physical quantities. A2 0 0 1 POSITION VECTOR TIME 2 VELOCITY vs TIME 3 DISPLACEMENT vs TIME (Uniform Velocity) (Constant Acceleration) (Uniform Acceleration) F) Slope = Slope = Slope = (instantaneous = velocity (constant) = acceleration velocity) (constant) t t t 0 t, 0 t, Key Point: Straight line constant velocity Key Point: Straight line constant acceleration Key Point: Parabolic uniform acceleration Steeper line greater velocity Above velocity in +ve direction Concave upward +ve acceleration Below velocity in -ve direction Concave downward - -ve acceleration 4 ACCELERATION vs TIME 5 SPEED vs TIME 6 vs y GRAPH (Uniform Acceleration) al speed (v) y Slope = y Area t Slope = V2 Change in tan 0 = acceleration 0 velocity (Av) Direction 0 of line t t O t, Key Point: line constant acceleration Key Point: Straight line constant acceleration Key Point: Gives direction of vector in 2D Area under curve change in velocity (Speed is scalar - always +ve) Angle with x-axis = tan (slope) 7 A + B 0 8 B 0 9 A X B| vs 0 (Magnitude of Resultant) (Dot Product) (Cross Product) + B| B A B| AB AB 0 0 0 -AB 0° 90° 0 180" 0° 90° Equation: Equation: = AB cos + = + + 2AB cos 0 Equation: = AB sin 0 Key Point: Key Point: Max (AB) at vectors in same direction Key Point: Max at 0 = = A + B Zero at vectors perpendicular Zero at & vectors parallel Min at 0 = = A Min (-AB) at 180° vectors opposite Max (AB) at 90° vectors perpendicular , VECTOR IN 3D (Direction Cosines) ANGLE BETWEEN TWO VECTORS TIPS TO REMEMBER Direction cosines: B - A Slope gives rate of change. A A A.B cos = Area under curve gives total change. A B Use sign of quantity to know direction. cos = B B Dot product related to cos 9. y + + cos2y 1