Question

The distance covered by a body in time $(5.0\pm 0.6)$ is $(40.0\pm 0.4)$m. Calculate the speed of the body. Also determine the percentage error in the speed.

Answer 1

Here $s=40.0\pm 0.4m$ and $t=5.0\pm 0.6s$. Therefore, speed,
$v=\frac{s}{t}=\frac{40.0}{5.0}=8.0m{s}^{-1}$
As $y=\frac{s}{t}$, therefore , $\frac{△v}{v}=\frac{△s}{s}+\frac{△t}{t}$
Here $△s=0.4m,s=40.0m,△t=0.6s,t=5.0s.$ Therefore,
or $\frac{△v}{v}=\frac{0.4}{40.0}+\frac{0.6}{5.0}\Rightarrow △v=[0.01+0.12]\times 8.0=1.04$
Hence, $v=(8.0\pm 1.04)m{s}^{-1}$; percentage error
$(\frac{△v}{v}\times 100)=0.13\times 100=13\%$