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. The acceleration due to gravity is the constant of variation. What is the acceleration due to gravity of a falling object? 4.9 9.8 10.2 19.6

Answer 1

It is given to us that 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 (which is not given to us). The acceleration due to gravity is the constant of variation. Now, we know, from basic physics that the value of the acceleration due to gravity in the SI unit is 9.8 m/s^2. Therefore, the second option is the correct option.

Answer 2

Correct option is b) $\rm 9.8 \; m/sec^2$

Step-by-step explanation:

Given :

Table -

Time (sec)                       Velocity (m/sec)

      0                                           0

      1                                           9.8

      2                                          19.6

      3                                           29.4

      4                                           39.2

Velocity varies directly with time.

Solution :

We know that,

$\rm v = u +at$ --- (1)

where, v is the final velocity in m/sec, u is the initial velocity in m/sec, a is the acceleration in $\rm m/sec^2$ and t is the time in sec.

So, from table we have

t = 1 sec, u = 0 m/sec, v = 9.8 m/sec

putting this values in equation (1), we get

$9.8=0+a(1)$

$\rm a = 9.8\;m/sec^2$

Therefore, option b) is correct.

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