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A body travels uniformly a distance (13....

A body travels uniformly a distance (`13.8+- 0.2`) m in a time (`4.0+- 0.3`) s. Calculate its velocity with error limits. What is the percentage error in velocity ?

Text Solution

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Given distance, `s = (13.8 +-0.2) m` and time `t= (4.0 +- 0.3) s`
Velocity `v= (s)/(t)= (13.8)/(4.0)= 3.45 m s^(-1)`
`(Deltav)/(v)= +- ((Deltas)/(s)+(Deltat)/(t))= +- ((0.2)/(13.8)+ (0.3)/(4.0))`
`= +- ((0.8 +4.14)/(13.8 xx 4.0))= +- (4.49)/(13.8 xx 4.0)= +-0.0895`
`Deltav=+0.0895 xx V= +-0.0895 xx 3.45 = +- 0.3087= +-0.31`
Hence `v= (3.5 + -0.31) m s^(-1)`
Percentage error in velocity = `(Deltav)/(v) xx 100 = +0.0895 xx 100 =+- 8.95% = +- 9%`
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