Error in acceleration
a = (v - u)/t. a is the acceleration, u the initial and v the final velocity, and t the time.
Error in a formula
Maximum error in a
0.3
a = 5.0 ± 0.36%
- v0.333 × 0.20.0667
- u0.333 × 0.20.0667
- t1.67 × 0.10.167
- Totaladd them0.3
This mixes a sum with a product, so it is worked out with the values: the sum of |slope| times error, the worst case.
a = 5.0 ± 0.3
Δa = |∂a/∂v| Δv + |∂a/∂u| Δu + |∂a/∂t| Δt
This mixes a sum with a product, so it is worked out with the values: the sum of |slope| times error, the worst case. A difference adds its absolute errors even though the values subtract, so a small difference of large numbers has a large percentage error.
Other formulas
Measured the same thing several times? Use repeated readings, or find the least count of your instrument.
Error in acceleration: quick answers
What is the formula for the error in acceleration?
a is the acceleration, u the initial and v the final velocity, and t the time. With a = (v - u)/t, the maximum error is given by Δa = |∂a/∂v| Δv + |∂a/∂u| Δu + |∂a/∂t| Δt. This mixes a sum with a product, so it is worked out with the values: the sum of |slope| times error, the worst case.
How do I work out the error with real numbers?
Take v = 20 ± 0.2 and u = 5 ± 0.2 and t = 3 ± 0.1. The maximum error in a is 0.0667 + 0.0667 + 0.167 = 0.3, so a = 5.0 ± 0.3.
Why are the errors added and never subtracted?
The error shown is the largest possible one. In the worst case every measurement is off in the direction that pushes the result the same way, so the errors pile up. They are added even when the quantity is divided or subtracted.