1. Given data

• Mass of the body: $m = 2\,\text{kg}$
• Force acting on it: $\vec F = (2\hat i + 3\hat j + 5\hat k)\,\text{N}$
• Initial velocity: $\vec u = 0$ (starts from rest)
• Initial position: origin
• Time: $t = 4\,\text{s}$
• Final position: $(8, b, 20)$

2. Find acceleration

Using Newton's second law, $\vec a = \frac{\vec F}{m}$ So, $\vec a = \frac{1}{2}(2\hat i + 3\hat j + 5\hat k)$ $\vec a = (1\hat i + 1.5\hat j + 2.5\hat k)\,\text{m/s}^2$

Thus,

• $a_x = 1$
• $a_y = 1.5$
• $a_z = 2.5$

3. Use equation of motion for displacement

Since initial velocity is zero and initial position is origin, $\vec r = \frac{1}{2}\vec a t^2$ At $t=4\,\text{s}$, $\vec r = \frac{1}{2}\vec a (4)^2 = 8\vec a$ So, $\vec r = 8(1\hat i + 1.5\hat j + 2.5\hat k)$ $\vec r = (8\hat i + 12\hat j + 20\hat k)$

Hence the coordinates after 4 s are $(8, 12, 20)$ So, $b = 12$

4. Rounded to nearest integer

$12$

5. Comparison with stored answer

Stored correct answer = $12$

This matches our derived answer.