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 ?

A body travels uniformly a distance (13.8+-0.2) m in a time (4.0+- 0.3

1.	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 ?
Answer» Solution :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%`