Question

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.
velocity of a falling object

time (seconds)	velocity (meters/second)
1	9.8
2	19.6
3	29.4
4	39.2

the acceleration due to gravity is the constant of variation. what is the acceleration due to gravity of a falling object?

• $4.9 \frac{m}{s^2}$
• $9.8 \frac{m}{s^2}$
• $10.2 \frac{m}{s^2}$
• $19.6 \frac{m}{s^2}$

Explanation:

Step1: Recall Direct Variation

For direct variation, \( v = kt \), where \( v \) is velocity, \( t \) is time, and \( k \) is the constant (acceleration here).

Step2: Calculate \( k \)

Using \( t = 1 \), \( v = 9.8 \): \( k=\frac{v}{t}=\frac{9.8}{1}=9.8 \frac{m}{s^2} \).
Check with \( t = 2 \), \( v = 19.6 \): \( k=\frac{19.6}{2}=9.8 \), consistent.

Answer:

B. \( 9.8 \frac{m}{s^2} \)