Question

Which of the following option gives correct vector form for equation v² = u² + 2as?
1. \(\overrightarrow{v} \times \overrightarrow{v}=\overrightarrow{u}\times \overrightarrow{u}+2\overrightarrow{a} \times \overrightarrow{s}\)
2. \(\overrightarrow{v} \times \overrightarrow{v}=\overrightarrow{u}\times \overrightarrow{u}+2\overrightarrow{a} . \overrightarrow{s}\)
3. \(\overrightarrow{v}.\overrightarrow{v}=\overrightarrow{u}.\overrightarrow{u}+2\overrightarrow{a} \times \overrightarrow{s}\)
4. \(\overrightarrow{v}.\overrightarrow{v}=\overrightarrow{u}.\overrightarrow{u}+2\overrightarrow{a}.\overrightarrow{s}\)

Answer 1

Correct Answer - Option 4 : \(\overrightarrow{v}.\overrightarrow{v}=\overrightarrow{u}.\overrightarrow{u}+2\overrightarrow{a}.\overrightarrow{s}\)

CONCEPT: ​.

• Equations of motion describe the behavior of a physical system in terms of its motion as a function of time.
• The equations of motion in the vector form are written as:

\(\overrightarrow{v}=\overrightarrow{u}+\overrightarrow{a}t\)

\(\overrightarrow{s}=\overrightarrow{u}t+{1 \over 2} \overrightarrow{a}t^2\)

\(\overrightarrow{v}.\overrightarrow{v}=\overrightarrow{u}.\overrightarrow{u}+2\overrightarrow{a}.\overrightarrow{s}\)

EXPLANATION:

The third equation of motion v2 = u2 + 2as in the vector form is written as:

\(\overrightarrow{v}.\overrightarrow{v}=\overrightarrow{u}.\overrightarrow{u}+2\overrightarrow{a}.\overrightarrow{s}\)

\(vv ~cos0 =uu ~cos0 + 2as ~cos0 \)

\(v^2 =u^2+ 2as \)

So the correct answer is option 4.