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Question #42058

Difficulty: 8/10 | 🟢 Free

The Question

A particle of mass $m = 1 \text{ kg}$ and charge $q = 1 \text{ C}$ is initially at rest at the origin. It is subjected to a time-varying electric field $\vec{E}(t) = E_x(t)\hat{i} + E_y(t)\hat{j}$ . The components of the electric field are given by: $E_x(t) = \begin{cases} 6t & 0 \le t \le 1 \\ 3(3-t) & 1 < t \le 3 \\ 0 & t > 3 \end{cases}$ $E_y(t) = \begin{cases} 0 & 0 \le t \le 3 \\ 3(t-3) & 3 < t \le 5 \\ 6(6-t) & 5 < t \le 6 \\ 0 & t > 6 \end{cases}$ where $E_x$ and $E_y$ are in $\text{V/m}$ and $t$ is in seconds. What is the position vector of the particle at $t = 7 \text{ s}$ ?

Options

A.
$(51\hat{i} + 21\hat{j}) \text{ m}$
B.
$(49.5\hat{i} + 22.5\hat{j}) \text{ m}$
C.
$(15\hat{i} + 12\hat{j}) \text{ m}$
D.
$(51\hat{i} + 24\hat{j}) \text{ m}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Area Under Acceleration-Time|Trajectory of Charged Particle|Vector Calculus

Why This Question Is Tricky

Common Mistakes

This question tests the ability to integrate piecewise acceleration in 2D kinematics without falling into the trap of applying constant acceleration (SUVAT) formulas to asymmetric pulses.

Students often incorrectly assume that a triangular acceleration pulse yields the same displacement as its average acceleration, which is only true for symmetric pulses (Trap B).

Furthermore, the problem evaluates the cross-coupling of time intervals: students frequently forget that after an acceleration pulse ends, the acquired velocity remains constant and continues to contribute to displacement in that axis while the other axis undergoes its own acceleration phase (Trap C).

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	Area Under Acceleration-Time
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free