Question

A body travels uniformly a distance of $(13.8\pm 0.2)m$ in a time $(4.0\pm 0.3)s$. Its velocity with error limits is

• A. (3.5 $\pm$ 0.6) m $s^{-1}$
• B. (3.5 $\pm$ 0.3) m $s^{-1}$
• C. (6.1 $\pm$ 0.6) m $s^{-1}$
• D. (6.1 $\pm$ 0.3) m $s^{-1}$

Answer 1

The correct option is B (3.5 $\pm$ 0.3) m $s^{-1}$

Distance covered $d=(13.8\pm 0.2)m$

Time taken $t=(4.0\pm 0.3)s$

Velocity $v=\frac{d}{t}$

So, absolute value of velocity $v=\frac{13.8}{4.0}=3.5m/s$

Error in velocity $\frac{\Delta v}{v}=\frac{\Delta d}{d}+\frac{\Delta t}{t}$

Or $\frac{\Delta v}{3.5}=\frac{0.2}{13.8}+\frac{0.3}{4}$

$⟹\Delta v=0.3m/s$

Thus, velocity is written as $(3.5\pm 0.3)m/s$