Q.6 Velocity of an object fired directly in upward direction is given by
V = 80 − 32t, where t (time) is in seconds.
When will the velocity be between 32 m/sec and 64 m/sec?
Introduction
Problems based on velocity–time equations and inequalities frequently appear in
board exams and competitive tests such as JEE and NEET. These questions test understanding of
linear equations, inequalities, and interval analysis.
In this article, we determine the time interval during which the velocity of an object lies
between 32 m/s and 64 m/s, using a step-by-step method and
detailed option analysis.
Key Concept Used
Since velocity must lie between two given values, we express the condition using a
double inequality:
32 ≤ V ≤ 64
Substituting the given expression for velocity allows us to solve for the valid time interval.
Step-by-Step Solution
Step 1: Form the inequality
32 ≤ 80 − 32t ≤ 64
Step 2: Subtract 80 from all parts
32 − 80 ≤ −32t ≤ 64 − 80
−48 ≤ −32t ≤ −16
Step 3: Divide by −32
(Inequality signs reverse when dividing by a negative number)
3⁄2 ≥ t ≥1⁄2
Step 4: Write the interval in increasing order
1⁄2 ≤ t ≤3⁄2
Final Answer
The velocity lies between 32 m/s and 64 m/s for:
t ∈ (1⁄2,3⁄2)
👉 Correct Option: (C)
Quick Exam Tip
For velocity problems involving inequalities:
- Always form a double inequality
- Be careful while dividing by negative numbers
- Check interval limits logically
Conclusion
This problem clearly demonstrates how inequalities can be applied to motion equations.
By following a systematic approach, the correct time interval can be obtained easily,
making such questions reliable scoring opportunities in exams.
