Question

en el instante mostrado para el movimiento mecánico, determine la aceleración y su módulo.

a) \\(\vec{a} = +3 \hat{\mathrm{i}}\\ \mathrm{m/s^2}; a = 3\\ \mathrm{m/s^2}\\)
b) \\(\vec{a} = -3 \hat{\mathrm{i}}\\ \mathrm{m/s^2}; a = 3\\ \mathrm{m/s^2}\\)
c) \\(\vec{a} = -5 \hat{\mathrm{i}}\\ \mathrm{m/s^2}; a = 5\\ \mathrm{m/s^2}\\)
d) \\(\vec{a} = +5 \hat{\mathrm{i}}\\ \mathrm{m/s^2}; a = 5\\ \mathrm{m/s^2}\\)
e) \\(\vec{a} = +8 \hat{\mathrm{i}}\\ \mathrm{m/s^2}; a = 8\\ \mathrm{m/s^2}\\)

Explanation:

⚡ Using what you learned: graphical analysis of motion and acceleration

Step 1: Identify the acceleration vector

The acceleration vector is represented by the arrow labeled \( 3\text{ m/s}^2 \). Since the arrow points to the right, which is the positive direction along the X-axis:

$$ \vec{a} = +3\hat{\text{i}}\text{ m/s}^2 $$

Step 2: Determine the magnitude of the acceleration

The magnitude (módulo) of the acceleration vector is its absolute value:

$$ a = |\vec{a}| = 3\text{ m/s}^2 $$

Answer:

A) \( \vec{a} = +3\hat{\text{i}}\text{ m/s}^2 \); \( a = 3\text{ m/s}^2 \)