PYQ + trends
1. TITLE
NEET 2023 Q7: Bullet Penetration — Full solution + Why they asked this
2. THE ACTUAL NEET QUESTION
NEET 2023 — Question
A bullet from a gun is fired on a rectangular wooden block with velocity u. When bullet travels 24cm through the block along its length horizontally, velocity of bullet becomes u/3. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:
A) 24cm
B) 28cm
C) 30cm
D) 27cm
3. OFFICIAL ANSWER
NEET Answer Key: (D)
4. COMPLETE SOLUTION
Step-by-step calculation:
This problem requires breaking the motion into two phases. Let the uniform retardation inside the block be $a$.
Phase 1 (First 24 cm):
* Initial velocity = $u$
* Final velocity = $u/3$
* Displacement ($s_1$) = $24\text{ cm}$
Using the third equation of motion: $v^2 = u^2 - 2as$
$(\frac{u}{3})^2 = u^2 - 2a(24)$
$\Rightarrow 48a = u^2 - \frac{u^2}{9} = \frac{8u^2}{9}$
$\Rightarrow 2a(24) = \frac{8u^2}{9}$ --- (Equation 1)
Phase 2 (Remaining distance to stop):
* Initial velocity = $u/3$
* Final velocity = $0$ (since it comes to rest)
* Displacement = $s_2$
Using the same equation: $0^2 = (\frac{u}{3})^2 - 2as_2$
$\Rightarrow 2as_2 = \frac{u^2}{9}$ --- (Equation 2)
Dividing Equation 1 by Equation 2:
$\frac{2a(24)}{2as_2} = \frac{\frac{8u^2}{9}}{\frac{u^2}{9}}$
$\Rightarrow \frac{24}{s_2} = 8$
$\Rightarrow s_2 = 3\text{ cm}$
The question asks for the total length of the block, which is the sum of both distances:
$\text{Total Length} = 24\text{ cm} + 3\text{ cm} = 27\text{ cm}$.
Formula used:
$v^2 = v_0^2 + 2ax$ (Kinematic equation for constant acceleration/retardation).
Why this approach:
Because time ($t$) is neither given nor asked for, the third kinematic equation, which directly relates velocity, acceleration, and displacement, is the perfect and fastest choice.
5. WHY NEET ASKED THIS
Explain the examiner's intent:
* What concept were they testing? They were testing the application of kinematic equations to uniformly retarded motion, specifically the concept of "stopping distance" where deceleration is assumed constant.
* What's the common mistake they expected students to make? The examiner expected students to correctly calculate the remaining distance ($3\text{ cm}$) but forget to read the final line of the question. Students frequently mark $3\text{ cm}$ or make ratio errors.
* Which option was the "trap"? Option A (24cm) is a trap for those who might mistakenly think the bullet stopped at the first checkpoint. Though $3\text{ cm}$ wasn't in the options, a slight calculation error leading to $4\text{ cm}$ would lead students directly into the trap of Option B (28cm).
6. TREND ANALYSIS
| Year | How they asked | Twist |
| 2024 | Calculus & Position-Time | Tested derivatives $v = \frac{dx}{dt}$ and $a = \frac{dv}{dt}$ instead of basic kinematic equations. |
| 2023 | Block Penetration (Kinematics) | Asked for the total block length rather than just the stopping distance. |
| 2022 | Free Fall & Galilean Ratios | Asked for distance ratios in specific seconds (1:3:5:7) utilizing direct free-fall formulas. |
Prediction for NEET 2026:
Expect a variation on Stopping Distance & Reaction Time. The concept that stopping distance is proportional to the square of initial velocity ($d_s \propto v_0^2$) is heavily emphasized in the material. You might see a question combining a driver's reaction time with the braking distance to find the total distance traveled before stopping.
7. SIMILAR QUESTIONS TO PRACTICE
"If you understood this, you can solve:"
* NEET 1998 Q42: A car moving at $40\text{ km/h}$ stops in $2\text{ m}$. Find minimum stopping distance at $80\text{ km/h}$. (Tests the exact same $v^2 \propto s$ principle).
* NEET 2020 Q14: A ball is thrown downwards at $20\text{ m/s}$ from a tower and hits the ground at $80\text{ m/s}$. Find the height. (Tests the identical equation $v^2 = u^2 + 2gh$).
* Topic with variation: Stopping distance questions where speed is tripled, checking if you know the distance increases by a factor of 9.
8. QUICK REVISION FOR THIS TYPE
For Bullet Penetration & Stopping Distance questions, always:
* First check: Is time mentioned? If not, immediately write down $v^2 = u^2 + 2as$.
* Then apply: Set up two equations. One for the first phase (velocity loss) and one for the second phase (coming to rest). Divide them to cancel out the unknown acceleration ($a$).
* Watch out for: What the question is actually asking. Highlight whether they want the "additional penetrating distance" ($s_2$) or the "total length/distance" ($s_1 + s_2$).
9. NCERT BASE
This question tests: NCERT Class 11, Chapter 2, Page 18 (Eq 2.8: $v^2 = v_0^2 + 2ax$) and Page 21 (Example 2.6: Stopping distance of vehicles).
10. CTA
All PYQs from this chapter → Kinematics Guide
Practice similar questions → Mock exams