In ECET 2026, Mathematics questions linked with Physics applications (motion, velocity, acceleration, force, etc.) are very scoring. Derivatives act as a bridge between Maths and Physics.
📘 Concept Notes
🌟 What is a Derivative in Physics?
- A derivative measures the rate of change of a physical quantity.
- In Physics, most formulas involving motion, forces, and energy use derivatives.
⚙️ Core Formulas
- Velocity from Displacement
Acceleration from Velocity
Newton’s 2nd Law (via derivative)
Work Done (Force × Displacement)
If force depends on displacement:
Power as Derivative of Work
Momentum
📐 Examples
Example 1:
If 
, find velocity and acceleration at 
.
- Velocity:
At
, 
- Acceleration:
Constant acceleration =
Example 2:
If force 
, find work done from 
to 
.
![W = \int_0^4 2x , dx = [x^2]_0^4 = 16 , J](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-56f7d39968e311189f8106de096f2b2f_l3.png "Rendered by QuickLaTeX.com")
🔟 10 Expected MCQs – ECET 2026
Q1. If 
, velocity at 
is:
A) 2
B) 4
C) 6
D) 12
Q2. Acceleration is the derivative of:
A) Displacement
B) Velocity
C) Force
D) Momentum
Q3. If velocity 
, then acceleration = ?
A) 2
B) 4
C) 8
D) Constant 4
Q4. Force is derivative of:
A) Momentum
B) Energy
C) Displacement
D) Work
Q5. Work done from 
from 
to 
is:
A) 4 J
B) 6 J
C) 8 J
D) 8/3 J
Q6. Power is derivative of:
A) Momentum
B) Velocity
C) Work
D) Acceleration
Q7. If displacement 
, velocity is:
A) cos t
B) –cos t
C) sin t
D) –sin t
Q8. For constant mass, 
A) m × v
B) m × a
C) m × s
D) m × p
Q9. If 
, acceleration at 
is:
A) 2
B) 3
C) 6
D) 9
Q10. Unit of derivative 
is:
A) m/s
B) m/s²
C) kg·m/s
D) N
✅ Answer Key
| Q.No | Answer |
|---|---|
| Q1 | D |
| Q2 | B |
| Q3 | B |
| Q4 | A |
| Q5 | C |
| Q6 | C |
| Q7 | A |
| Q8 | B |
| Q9 | C |
| Q10 | A |
🧠 Explanations
- Q1 → D:
, at 
. - Q2 → B: Acceleration is derivative of velocity.
- Q3 → B:
. - Q4 → A:
. - Q5 → C:
![W = \int_0^2 3x^2 dx = [x^3]_0^2 = 8](https://learnnewthings.fun/wp-content/ql-cache/quicklatex.com-942606b721bfa69a231e81c86688cc64_l3.png "Rendered by QuickLaTeX.com")
. - Q6 → C:
. - Q7 → A:
. - Q8 → B:
. - Q9 → C:
. - Q10 → A: Derivative of displacement w.r.t time = velocity (m/s).
🎯 Why Practice Matters
- Derivative-based Physics applications are straightforward but often carry 2–3 marks.
- Strong grip on velocity, acceleration, force, and work-energy derivatives ensures easy scoring.
