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Motion in a Straight Line — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Straight Line1 Mark
MCQ
A person travelling on a straight line moves with a uniform velocity $v_1$ for some time and with uniform velocity $v_2$ for the next equal time. The average velocity is given by:
  • ✓
    $\text{v}=\frac{\text{v}_1+\text{v}_2}{2}$
  • B
    $\text{v}=\sqrt{\text{v}_1\text{v}_2}$
  • C
    $\frac{2}{\text{v}}=\frac{1}{\text{v}_1}+\frac{1}{\text{v}_2}$
  • D
    $\frac{1}{\text{v}}=\frac{1}{\text{v}_1}+\frac{1}{\text{v}_2}$
✓

Answer

Correct option: A.
$\text{v}=\frac{\text{v}_1+\text{v}_2}{2}$
$a.\ \text{v}=\frac{\text{v}_1+\text{v}_2}{2}$
Explanation:
Velocity is uniform in both cases; that is, acceleration is zero.
We have:
$\text{d}_1=\text{v}_1\text{t}$ and $\text{d}_2=\text{v}_2\text{t}$
Total displacement, $\text{d = d}_1+\text{d}_2$
Total time, $\text{t = t + t = 2t}$
$\therefore$ Average velocity, $\text{v}=\frac{\text{d}_1+\text{d}_2}{2\text{t}}=\frac{\text{v}_1+\text{v}_2}{2}$

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