Acceleration & Time-to-Speed
Top speed is the wrong number for a 12-foot field. This works out how long you actually take to get anywhere, and how much of your quoted speed you never see.
Inputs
The full size V5 motor. Most drivetrains are built from these.
The smaller V5 motor. It gives roughly half the torque, so two of them are worth about one of the big ones.
Diameter across the wheel. Mecanum and flex wheels share a diameter with the plain ones, so pick by name rather than by size. Anything not listed can be typed in.
Caps how hard you can accelerate before the wheels spin.
Results
Time to cross the field
—sec
144 inches from a standstill.
If you ignored acceleration
—sec
Acceleration costs you
—%
Time to cross one tile
—sec
24 inches.
Time to reach 95% of top speed
—sec
Distance used getting there
—in
Top speed
—ft/s
Starting acceleration
—g
How this is calculated
A robot does not leave the line at its top speed. It builds up to it, and over twelve feet a surprising share of the run is spent still building. That is why two robots with the same quoted ft/s can be visibly different across a field.
Two forces, and the smaller one wins
At any instant the force pushing the robot forward is whichever of these is smaller:
from the motors F = (motors × stall torque × ratio ÷ radius) × (1 − v ÷ v_top) from the floor F = grip × weightWith your numbers
The motor term starts high and falls to zero as you approach top speed. That is the same torque curve as the stall calculator. The traction term is flat. So a strong drive usually spends its first moments traction-limited, wheels on the edge of slipping, then hands over to the motor curve as speed builds.
Why this is simulated rather than solved
Because the governing force switches between those two expressions partway through, there is no single tidy formula for the whole run. This page steps through the motion in half-millisecond intervals, recalculating force and speed each step, and reports where the robot actually was. That is both more honest and easier to check than an algebraic result that hides the switchover.
The part worth taking away
Compare the field crossing time with the naive figure. The gap is time you lose to physics that a top-speed number simply does not mention. It grows with a heavier robot, and it grows with a higher top speed. The faster the drive, the larger the share of the field spent getting there.
This is the real argument against chasing extreme gear ratios. Past a point, a higher top speed buys nothing over twelve feet because you never reach it, while the torque you gave up costs you on every start.
Sources & assumptions
Stall torque is published for the 100 RPM cartridge andderived for the others by inverse scaling with speed. Free speeds and wheel diameters are VEX published figures. The field is 144" square with 24" tiles.
The friction coefficient is estimated, since no VEX figure exists. It sets the traction ceiling, so it matters most in the first moments of the run and barely at all near top speed.
Uses a linear torque-speed curve and forward Euler integration at 0.5 ms steps, which is far finer than needed for the accuracy claimed here.
- Purdue SIGBots Wiki — VEX Motors — checked 2026-08-17
- VEX Robotics — V5 Smart Motor & Gear Cartridges (276-4840) — checked 2026-08-17
- VEX Library — Understanding VEX V5 Wheels — checked 2026-08-17
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