Kinematics

Position of a body moving at constant velocity.

Final velocity in terms of initial velocity, uniform acceleration, and time.

Displacement in terms of initial velocity, acceleration, and time.

Displacement per unit time over a finite interval.

Relates final velocity to initial velocity, acceleration, and displacement.

Change in velocity per unit time over a finite interval.

Velocity at a specific instant — the derivative of position with respect to time.

Total time a projectile remains in the air when launched from and landing on level ground.

Greatest vertical height reached by a projectile launched from level ground.

Acceleration at a specific instant — the derivative of velocity with respect to time.

Horizontal range on level ground. Maximum range at θ = 45°.

Velocity of A as observed from B.

Horizontal and vertical velocity components at any time t.

Magnitude of velocity vector at any instant during projectile motion.

Direction of velocity vector with respect to horizontal at any instant.

Horizontal and vertical coordinates of a projectile at time t.

Path of a projectile — a downward-opening parabola.

Time for a horizontally projected body to fall height h.

Horizontal distance covered by a body projected horizontally from height h.

Speed of a horizontally projected body at time t.

Parabolic path of a horizontally projected body.

Time of flight when projected at angle θ from height h above ground.

Horizontal range when projected at angle θ from height h.

Equation of path when projected at angle θ from height h.

Range along an inclined plane when projected up the slope. α = projection angle from horizontal, β = inclination angle.

Range along an inclined plane when projected down the slope.

Maximum range achievable on an inclined plane of angle β.

Velocity of a projectile launched from a moving body — vector addition of body velocity and launch velocity.

Air resistance reduces range, maximum height, and time of flight. Optimal angle shifts below 45°.

Gives the average speed of an object as total distance traveled divided by total time taken.

Gives the magnitude of the resultant of two vectors inclined at an angle theta to each other.

Gives the magnitude of the subtraction vector of two vectors inclined at an angle theta.

Gives the dot product of two vectors in terms of their magnitudes and included angle or rectangular components.

Gives the magnitude of the projection of vector A along the direction of vector B.

Gives the radial acceleration directed toward the centre for an object moving in a circle of radius R with speed v.