QUARTER FINAL STAGE 2024
Accra Academy: 45 points
Oyoko Methodist SHS: 36 points
St. Joseph Seminary SHS: 28 points
ROUND 2 - SPEED RACE
QUESTION
Find the magnitude of the acceleration of a $0.5\text{ kg}$ object on which the net force $15\mathbf{j} -20\mathbf{k}$ N acts.
ANSWER: 50 m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{15^2 + (-20)^2}$
$|\mathbf{F}| = \sqrt{225 + 400}$
$|\mathbf{F}| = \sqrt{625}$
$|\mathbf{F}| = 25\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{25}{0.5}$
$a = \dfrac{25}{5\times10^{-1}}$
$a = 50\text{ m/s}^2$
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PRACTICE QUESTIONS
1. QUESTION: Find the magnitude of the acceleration of a 0.500 kg object on which the net force $3.00\mathbf{j}+4.00\mathbf{k}$ N acts.
ANSWER: 10.0 m/s² or $1.00\times10^{1}$ m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(3.00)^2 + (4.00)^2}$
$|\mathbf{F}| = \sqrt{25.0}$
$|\mathbf{F}| = 5.00\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{5.00}{0.500}$
$a = \dfrac{5}{5\times10^{-1}}$
$a = 10.0\text{ m/s}^2\text{}$
2. QUESTION: Find the magnitude of the acceleration of a 2.0 kg object on which the net force $3.0\mathbf{j}+4.0\mathbf{k}$ N acts.
ANSWER: 2.5 m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(3.0)^2 + (4.0)^2}$
$|\mathbf{F}| = \sqrt{9.0 + 16}$
$|\mathbf{F}| = \sqrt{25}$
$|\mathbf{F}| = 5.0\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{5.0}{2.0}$
$a = 2.5\text{ m/s}^2$
3. QUESTION: Find the magnitude of the acceleration of a 1.0 kg object on which the net force $5.0\mathbf{j}+12\mathbf{k}$ N acts.
ANSWER: 13 m/s² or $1.3\times10^{1}$ m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(5.0)^2 + (12)^2}$
$|\mathbf{F}| = \sqrt{169}$
$|\mathbf{F}| = 13\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{13}{1.0}$
$a = 13\text{ m/s}^2\text{}$
4. QUESTION: Find the magnitude of the acceleration of a 3.0 kg object on which the net force $9.0\mathbf{j}+12\mathbf{k}$ N acts.
ANSWER: 5.0 m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(9.0)^2 + (12)^2}$
$|\mathbf{F}| = \sqrt{225}$
$|\mathbf{F}| = 15\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{15}{3.0}$
$a = 5.0\text{ m/s}^2\text{}$
5. QUESTION: Find the magnitude of the acceleration of a 1.0 kg object on which the net force $8.0\mathbf{j}+15\mathbf{k}$ N acts.
ANSWER: 17 m/s² or $1.7\times10^{1}$ m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(8.0)^2 + (15)^2}$
$|\mathbf{F}| = \sqrt{289}$
$|\mathbf{F}| = 17\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{17}{1.0}$
$a = 17\text{ m/s}^2\text{}$
6. QUESTION: Find the magnitude of the acceleration of a 0.50 kg object on which the net force $1.8\mathbf{j}+2.4\mathbf{k}$ N acts.
ANSWER: 6.0 m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(1.8)^2 + (2.4)^2}$
$|\mathbf{F}| = \sqrt{3.24 + 5.76}$
$|\mathbf{F}| = \sqrt{9.0}$
$|\mathbf{F}| = 3.0\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{3.0}{0.50}$
$a = \dfrac{3}{5\times10^{-1}}$
$a = \dfrac{3}{5} \times10^{1}$
$a = 6.0\text{ m/s}^2$
7. QUESTION: Find the magnitude of the acceleration of a 5.0 kg object on which the net force $7.0\mathbf{j}+24\mathbf{k}$ N acts.
ANSWER: 5.0 m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(7.0)^2 + (24)^2}$
$|\mathbf{F}| = \sqrt{625}$
$|\mathbf{F}| = 25\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{25}{5.0}$
$a = 5.0\text{ m/s}^2\text{}$
8. QUESTION: Find the magnitude of the acceleration of a 2.5 kg object on which the net force $15\mathbf{j}+8.0\mathbf{k}$ N acts.
ANSWER: 6.8 m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(15)^2 + (8.0)^2}$
$|\mathbf{F}| = \sqrt{289}$
$|\mathbf{F}| = 17\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{17}{2.5}$
$a = \dfrac{17}{25\times10^{-1}}$
$a = \dfrac{17}{25} \times10^{1}$
$a = 6.8\text{ m/s}^2\text{}$
9. QUESTION: Find the magnitude of the acceleration of a 1.0 kg object on which the net force $21\mathbf{j}+28\mathbf{k}$ N acts.
ANSWER: 35 m/s² or $3.5\times10^{1}$ m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(21)^2 + (28)^2}$
$|\mathbf{F}| = \sqrt{1225}$
$|\mathbf{F}| = 35\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{35}{1.0}$
$a = 35\text{ m/s}^2\text{}$
10. QUESTION: Find the magnitude of the acceleration of a 5.0 kg object on which the net force $3.6\mathbf{j}+4.8\mathbf{k}$ N acts.
ANSWER: 1.2 m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(3.6)^2 + (4.8)^2}$
$|\mathbf{F}| = \sqrt{12.96 + 23.04}$
$|\mathbf{F}| = \sqrt{36}$
$|\mathbf{F}| = 6.0\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{6.0}{5.0}$
$a = 1.2\text{ m/s}^2$
11. QUESTION: Find the magnitude of the acceleration of a 5.0 kg object on which the net force $15\mathbf{j}+36\mathbf{k}$ N acts.
ANSWER: 7.8 m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(15)^2 + (36)^2}$
$|\mathbf{F}| = \sqrt{1521}$
$|\mathbf{F}| = 39\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{39}{5.0}$
$a = 7.8\text{ m/s}^2\text{}$
12. QUESTION: Find the magnitude of the acceleration of a 1.5 kg object on which the net force $0.90\mathbf{j}+1.2\mathbf{k}$ N acts.
ANSWER: 1.0 m/s²
SOLUTION:
$|\mathbf{F}| = \sqrt{F_y^2 + F_z^2}$
$|\mathbf{F}| = \sqrt{(0.90)^2 + (1.2)^2}$
$|\mathbf{F}| = \sqrt{0.81 + 1.44}$
$|\mathbf{F}| = \sqrt{2.25}$
$|\mathbf{F}| = 1.5\text{ N}$
$a = \dfrac{|\mathbf{F}|}{m}$
$a = \dfrac{1.5}{1.5}$
$a = \dfrac{15}{15}$
$a = 1.0\text{ m/s}^2$