the velocity of an object in meters per second varies directly with time in seconds since the object was…

the velocity of an object in meters per second varies directly with time in seconds since the object was dropped, as represented by the table.\n\nvelocity of a falling object\n| time (seconds) | velocity (meters/second) |\n| ---- | ---- |\n| 0 | 0 |\n| 1 | 9.8 |\n| 2 | 19.6 |\n| 3 | 29.4 |\n| 4 | 39.2 |\n\nthe acceleration due to gravity is the constant of variation. what is the acceleration due to gravity of a falling object?\n○ 4.9 $\frac{m}{s^{2}}$\n○ 9.8 $\frac{m}{s^{2}}$\n○ 10.2 $\frac{m}{s^{2}}$\n○ 19.6 $\frac{m}{s^{2}}$

the velocity of an object in meters per second varies directly with time in seconds since the object was dropped, as represented by the table.\n\nvelocity of a falling object\n| time (seconds) | velocity (meters/second) |\n| ---- | ---- |\n| 0 | 0 |\n| 1 | 9.8 |\n| 2 | 19.6 |\n| 3 | 29.4 |\n| 4 | 39.2 |\n\nthe acceleration due to gravity is the constant of variation. what is the acceleration due to gravity of a falling object?\n○ 4.9 $\frac{m}{s^{2}}$\n○ 9.8 $\frac{m}{s^{2}}$\n○ 10.2 $\frac{m}{s^{2}}$\n○ 19.6 $\frac{m}{s^{2}}$

Answer

Explanation:

Step1: Definir la fórmula de aceleración

La aceleración $a$ se define como el cambio en la velocidad $\Delta v$ dividido por el cambio en el tiempo $\Delta t$, es decir $a=\frac{\Delta v}{\Delta t}$.

Step2: Elegir dos puntos de la tabla

Tomemos los puntos $(t_1 = 0, v_1=0)$ y $(t_2 = 1, v_2 = 9.8)$.

Step3: Calcular la aceleración

Sustituimos en la fórmula: $a=\frac{v_2 - v_1}{t_2 - t_1}=\frac{9.8 - 0}{1 - 0}=9.8\frac{m}{s^2}$.

Answer:

$9.8\frac{m}{s^2}$