acceleration = a = F / m => F = m * a
Let us say in measurements of acceleration and mass the errors are Δa and Δm respectively. The errors come in because of the minimum count of measuring instruments like a scale (least count of 1 mm). Let the resulting error in Force that is calculated be ΔF.
F + ΔF = (m +Δm) (a + Δa)
= m a + a Δm + m Δa + Δm Δa
Δm Δa is usually very very small as compared to other quantities on RHS. We take absolute values of Δm and Δa, as we are interested in the maximum error on the positive or negative side.
=> ΔF = a Δm + m Δa
=> ΔF/F = Δm / m + Δa / a
=> ΔF/F * 100 = Δm / * 100 + Δa / a * 100
a = F / m
Δa / a * 100 = ΔF / F * 100 + Δm/m * 100
% error in a = % error in F + % error in m
ΔF = 5 units Δm = 0.2 units
%error in a = 5/100 * 100 + 0.2 /10 * 100
Force a = F / m = 100 / 10 = 10 m/sec² This is what is measured and calculated using the instruments and equipment we have.
While reporting this value of a , we say that it is :
a = 10 +- 7% m/sec² , or a = 10 +- 0.7 m/sec²
OR, relative error in a
= relative error in measurement of F + relative error in measurement of m