Concept:
A growth curve represents:
\[
\text{Changes in growth over time}
\]
Velocity growth curve specifically measures:
\[
\text{Rate of growth at different ages}
\]
To study growth velocity accurately, repeated observations of the same individuals are necessary.
Step 1: Understanding Longitudinal Study.
A longitudinal study involves:
• Observing the same individuals repeatedly,
• Recording measurements over long periods,
• Tracking growth changes through time.
This method is ideal for:
\[
\text{Growth velocity analysis}
\]
because growth rate can only be calculated when continuous measurements are available.
Thus:
\[
\boxed{\text{Longitudinal study}}
\]
is correct.
Step 2: Analyzing Cross-sectional Study.
Cross-sectional studies involve:
• Different individuals at different ages,
• Single-time observations.
They are useful for size comparisons but not ideal for:
\[
\text{Velocity growth curves}
\]
Thus incorrect.
Step 3: Analyzing Mixed Longitudinal Study.
Mixed longitudinal design combines:
• Cross-sectional,
• Longitudinal approaches.
Although useful in growth studies, the standard design specifically used for velocity growth curves is:
\[
\text{Longitudinal study}
\]
Hence this option is not the best answer.
Step 4: Analyzing Case Study.
Case study focuses on:
• Individual or small-group detailed analysis.
It is not generally used for population growth velocity curves.
Therefore incorrect.
Step 5: Final conclusion.
The study design employed for velocity growth curve analysis is:
\[
\boxed{\text{Longitudinal study}}
\]
Hence, the correct answer is:
\[
\boxed{\text{(A) Longitudinal study}}
\]