The distance covered by a body in time (5.0  ± 0.6)s is (40.0 ± 0.4)m.Calculate the speed of the body…

Q: The distance covered by a body in time (5.0  ± 0.6)s is (40.0 ± 0.4)m.Calculate the speed of the body. Also determine the percentage error in the speed.

Sol. Here, s=(40.0 ± 0.4)m and t=(5.0 ± 0.6)s

⇒ Speed v = s/t

v = 40.0/(5.0) = 8.0 m/s

As v = s/t

$\large \frac{\Delta v}{v} = \pm (\frac{\Delta s}{s} + \frac{\Delta t}{t})$

$\large \frac{\Delta v}{v} = \pm (\frac{0.4}{40.0} + \frac{0.6}{5.0}) = \pm 0.13 $

∆v = 0.13 × 8.0 = 1.04

Hence,v=(8.0 ± 1.04) m/s

∴ Percentage error $\large = \frac{\Delta v}{v} \times 100 $

$\large = 0.13 \times 100 $

= 13 %