By Zencalcy Editorial TeamLast reviewed About us
A sled on a slope accelerates under the downhill component of gravity and loses some of that to friction. If the slope is long enough to reach a steady speed, the run time and bottom speed follow from constant acceleration.
Speed at the bottom of a sledding slope.
a = g(sin θ − μ cos θ) v = √(2aL) t = √(2L / a)
This assumes a standing start and constant friction. Snow friction is typically 0.03 to 0.1 for a sled.
| Symbol | Meaning |
|---|---|
| θ | Slope angle above the horizontal. |
| L | Length of the run along the slope, in metres. |
| μ | Coefficient of friction. |
| v | Speed at the bottom, in metres per second. |
Acceleration is 9.80665 × (0.5 − 0.0866) = 4.054 m/s², so the sled reaches 9.01 m/s in about 2.22 s.
Continue with the SUVAT Calculator, Terminal Velocity Calculator, or the Time of Flight Calculator — or browse more kinematics tools and all physics calculators.
When μ is at least tanθ the sled stays put. The calculator reports zero acceleration in that case.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026