Find Time When Initial Velocity is Regained | Acceleration-Time Graph | JEE Physics | Doubtify JEE

 

⏱️ Acceleration-Time Graph – Find Time When Initial Velocity is Regained | JEE Physics | Doubtify JEE

❓ Question:

The acceleration-time graph of a particle is as shown. At what time does the particle acquire its initial velocity again?

📄 Solution Page Link:

---

🧠 Concept Behind the Question:

To solve this problem, we need to recall that velocity is the area under the acceleration-time (a–t) graph. The area under the graph from the beginning of motion till a certain time gives the change in velocity in that time interval.

• Positive area (above time axis) → velocity increases

• Negative area (below time axis) → velocity decreases

So, the total area from t = 0 to t = some time = 0, means the net change in velocity is zero.
This tells us that the particle has returned to its initial velocity.

---

📊 Step-by-Step Explanation:

Let’s say the particle starts with velocity v₀ at t = 0.

1. From 0 to some time t₁, acceleration is positive → velocity increases.

2. From t₁ to t₂, acceleration is negative → velocity decreases.

We want to find the time t where:

Net change in velocity = 0
⇒ Area under graph from 0 to t = 0

This happens when the area above the time axis (positive) and the area below (negative) are equal in magnitude.

👉 So visually, observe the graph carefully and calculate or compare areas geometrically.
Once the net area = 0, the velocity comes back to its initial value.

---

📝 Final Answer:

From the graph (shown in the solution), the areas balance out at a specific time t = ___ s

---

🎥 Video Solution:

---

🔍 Why This Question is Important:

• It’s a graph-based conceptual question that regularly appears in JEE Mains.

• Combines integration of acceleration and interpretation of graphical data.

• Tests your ability to visualize motion and apply physics meaningfully.

• Strengthens your grip on kinematics and calculus-based motion.

---

💬 Have a Doubt?

DM us on Instagram or mail us at doubtifyqueries@gmail.com – We’re here to help!

---

🎯 Pro Tip:

Always check unit consistency and area calculation in a–t graph questions. These are commonly used tricks in competitive exams like JEE.

---

Stay consistent. Watch – Pause – Solve – Repeat.
Team Doubtify is with you till the finish line! 💪