Kinetic Energy Calculator (Ek = ½mv²)
Calculate the kinetic energy of any moving object. Enter mass and velocity — get Ek in joules, kilojoules, kilocalories and momentum instantly. Formula: Ek = ½mv².
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Velocity and Acceleration Calculator (kinematics)
Kinematics is the branch of physics that describes the motion of objects. This calculator covers four fundamental formulas: average velocity (v = s / t), distance (s = v * t), time (t = s / v), and acceleration (a = (v - v0) / t). Select the mode, enter the known values, and the result is computed instantly. Velocity is shown in both m/s and km/h, distance in m and km, time in seconds and minutes, and acceleration in m/s² with a fraction-of-g indicator. Useful for students, engineers, drivers, and sports analysts.
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How we calculate velocity and acceleration
In "velocity" mode the calculator uses v = s / t, where s is distance in metres and t is time in seconds. The result in m/s is converted to km/h by multiplying by 3.6. In "distance" mode we compute s = v * t. The result in metres is also expressed in kilometres (divide by 1,000). In "time" mode we compute t = s / v. The result in seconds is also expressed in minutes (divide by 60). Division by zero is guarded — the calculator returns 0. In "acceleration" mode we compute a = (v - v0) / t. The result in m/s2 is also expressed as a fraction of g = 9.81 m/s2. All results are rounded to 4 significant figures.
Example: a car on the motorway
Example 1 — velocity: A car covers 180 km (180,000 m) in 7,200 s (2 h). Average velocity: v = 180,000 / 7,200 = 25 m/s = 90 km/h. Example 2 — acceleration: A car accelerates from 0 to 27.78 m/s (100 km/h) in 10 s. Acceleration: a = (27.78 - 0) / 10 = 2.778 m/s2 = 0.283 g. Example 3 — time: How long does a 300 km trip take at an average speed of 100 km/h (27.78 m/s)? t = 300,000 / 27.78 = 10,800 s = 180 min = 3 hours.
Frequently asked questions
What is average velocity?
Average velocity is the ratio of distance travelled to the time taken: v = s / t. It is expressed in m/s (SI) or km/h. It does not describe instantaneous changes in speed — it is an overall average over the entire journey.
How do you convert m/s to km/h?
Multiply the value in m/s by 3.6: v(km/h) = v(m/s) x 3.6. Example: 10 m/s = 36 km/h. The factor 3.6 follows from the definition of units (1 m/s = 3,600 m/h = 3.6 km/h). The calculator does this conversion automatically.
What is acceleration and what are its units?
Acceleration is the rate of change of velocity: a = (v - v0) / t. The SI unit is m/s2 (metres per second squared). Gravitational acceleration g = 9.81 m/s2 is a convenient reference — the calculator also shows the result as a fraction of g.
What does the g-fraction result mean?
The g-fraction tells you how many times larger or smaller the calculated acceleration is compared to Earth's gravitational acceleration g = 9.81 m/s2. For example, 4.905 m/s2 = 0.5 g. A value of 1 g equals the force of Earth's gravity.
How do you calculate distance given velocity and time?
Use s = v * t, where v is velocity in m/s and t is time in seconds. The result is given in metres and kilometres. Example: a vehicle travelling at 25 m/s (90 km/h) for 3,600 s (1 h) covers 90,000 m = 90 km.
How do you calculate travel time?
Use t = s / v, where s is distance in metres and v is velocity in m/s. The result is given in seconds and minutes. Example: a 150 km (150,000 m) trip at 25 m/s (90 km/h) takes 6,000 s = 100 minutes.
What is the typical acceleration of a passenger car?
A typical passenger car accelerates from 0 to 100 km/h (27.78 m/s) in about 8-12 seconds, corresponding to 2.3-3.5 m/s2 (0.23-0.36 g). Sports cars achieve 4-7 m/s2 (0.4-0.7 g). For comparison, emergency braking is around 8-10 m/s2 (0.8-1 g).
What is uniformly accelerated motion?
Uniformly accelerated motion is motion in which acceleration is constant over time. Velocity increases (or decreases) linearly with time. The kinematic formulas used in this calculator apply to this type of motion. In reality, forces such as air resistance and friction modify this behaviour.
Does the calculator account for air resistance?
No. The calculator uses ideal kinematics formulas (uniform or uniformly accelerated motion) without accounting for air resistance, friction, or external forces. Results are accurate for simplified physics problems; in real-world scenarios motion resistance should be considered.
What are the practical uses of this calculator?
The calculator is useful for school and university physics problems, GPS data analysis (average travel speed), sports calculations (sprinter pace, projectile velocity), mechanical engineering design, and everyday estimates of travel time and braking distance.
Results are for informational and educational purposes. The calculator uses classical kinematics formulas (uniform and uniformly accelerated motion) and does not account for air resistance, friction, or relativistic effects.