The formula of time in physics is : divide the distance by the speed. A runner covering 400 m at 8 m/s needs 50 s. This is the speed formula rearranged, and it answers every question that asks how long a trip lasts at a steady speed.
When the speed is changing, other time formulas take over. With a constant acceleration a, the time to go from u to v is . For an object dropped from rest through a height h, the fall time is . This page covers all three and shows which one a question is asking for.
Quick facts
Formula
With acceleration
Free fall from rest
SI unit
second (s)Dimensional formula
[M⁰ L⁰ T¹]Type
Scalar, a base quantity in SI
Time formula physics: which one to use
| Information given | Formula | Condition |
|---|---|---|
| Distance and steady speed | Speed constant, or use average speed | |
| Start velocity, end velocity, acceleration | Acceleration constant | |
| Height of a drop from rest | Air resistance ignored | |
| Displacement and both velocities | Acceleration constant |
The first row is the one most Class 9 and middle school questions want. The others come from the equations of motion. Time is a scalar and in physics problems it is always positive, so if a rearrangement gives a negative time, a sign was mishandled.
Examples using the formula of time
Example 1: a long train journey
A train travels 360 km at an average speed of 80 km/h. How long does the trip take?
That is 4 hours 30 minutes, or 16 200 s.
Example 2: light from the Sun
The Sun is about 1.496 × 10¹¹ m from Earth. Light travels at 3.00 × 10⁸ m/s. How long does sunlight take to reach us?
About 499 s, which is 8.3 minutes.
Example 3: braking to a stop
A car moving at 25 m/s brakes with a steady retardation of 5.0 m/s². How long until it stops?
m/s, , m/s².
Example 4: a stone dropped down a well
A stone falls from rest through 45 m. Find the fall time with g = 9.8 m/s².
Unit of time and its dimension
Time sits among the seven SI base quantities, with the second as its unit, so it is a base quantity, not a derived one. Its dimensional formula is simply [M⁰ L⁰ T¹], usually written [T]. Common conversions are 1 min = 60 s, 1 h = 3600 s and 1 day = 86 400 s. Convert to seconds before using any SI formula, and convert back at the end if the question wants hours or minutes.
A quick check of t = d/v: metres divided by metres per second leaves seconds, as it should.
Reading time from graphs
On a distance time graph or position time graph, time is the horizontal axis, so you read the time for a given position straight off it. On a velocity time graph, the time for an object to stop is where the line crosses the time axis. For a body thrown upward, that crossing is the moment it reaches the top, which links this page to the time of flight formula for projectiles.
Mistakes with time calculations
- Hours written as decimals of minutes. 4.5 h is 4 h 30 min, not 4 h 50 min.
- Mixed units. Kilometres divided by metres per second gives a meaningless number. Make the length units match.
- Forgetting the square root in the free fall formula.
- Ignoring the sign of a in t = (v − u)/a for a slowing object.
Related pages: the formula of speed, the distance formula physics page, the speed, distance and time triangle, and, for the rest of the motion chapter, kinematics formulas.
Frequently asked questions
What is the formula for time physics problems use most?
For steady speed, time = distance / speed, t = d / v. With constant acceleration, t = (v − u) / a.
In which unit is time measured in SI?
The second, symbol s. Minutes and hours are allowed in answers only if the question asks for them.
What is formula of time in free fall?
For an object dropped from rest from height h, t = √(2h / g), ignoring air resistance.
Does time have a direction like velocity does?
No. Time is a scalar, so a value such as 5 s carries no direction, and in these problems it is never negative.
What is the dimensional formula of time?
[M⁰ L⁰ T¹], usually written [T], because time is itself a base quantity.