Kinematics & Motion
Every kinematics & motion calculator on CalcEngines — each with its formula, a worked example, the standard it follows and the assumptions it makes.
9 calculators in this section
- Average Speed vs Average Velocity CalculatorAverage speed is total distance over total time. Average velocity is net displacement over total time. The headline here is the ratio of the two — one when the journey is a straight run, exactly zero when you end up where you started, and a verdict on how much your path doubled back.
- Equations of Motion Calculator: Any Three of u, v, a and tGive it any three of initial velocity u, final velocity v, acceleration a and time t. It returns the displacement s, fills in the fourth quantity you did not give, and names which of the four equations it used — which is the part a formula sheet never tells you.
- Free Fall and Vertical Motion Calculator: Both RootsThrow something straight up and it passes every height twice. s = ut − ½gt² is a quadratic in t, so it has two roots, and deciding which one the question wants is the mark. This page solves it, prints both roots, and tells you when there is no root at all.
- Motion Graphs: What the Slope and the Area Give YouPick a graph and pick a feature, and this page tells you which quantity it is — including the two cases where the answer is nothing at all. The area under a displacement–time graph is the most commonly computed meaningless number in school physics.
- Projectile Launched from a Height CalculatorLaunch from a cliff, a table or a balcony and the trajectory stops being symmetric: it falls for longer than it rises, lands faster and steeper than it left, and the best angle is no longer 45°. This page solves the unequal-heights quadratic and prints the range-maximising angle for your own launch height.
- Projectile Motion Calculator: Range, Height and Time of FlightLaunch speed and launch angle in; range, maximum height, time of flight, both velocity components and the complementary angle that gives the same range out. Level ground, no air resistance, and every trigonometric step taken in radians.
- Relative Velocity Calculator: One and Two DimensionsThe velocity of A relative to B is vA − vB — a vector subtraction, component by component, never a subtraction of speeds. Two cars at 20 and 15 m/s can approach at 35 m/s, separate at 5 m/s, or close at 25 m/s, and the only thing that decides which is the geometry.
- Stopping Distance Calculator: Reaction plus BrakingTotal stopping distance is two different functions of speed added together: a reaction distance that grows in proportion to speed and a braking distance that grows as the square of it. Double your speed and the first doubles while the second quadruples — which is the whole reason the total is not proportional to anything.
- Uniform Circular Motion CalculatorGive the radius and any one of speed, period, frequency or angular velocity, and the page returns the other three plus the centripetal acceleration and force. Uniform means the speed is constant, not the velocity — which is why there is an acceleration at all.