Velocity vs Time Graph For Freely Falling Object

In free fall, we assume that there's no air resistance. 

The velocity vs time graph for freely falling object is a straight line passing through origin with positive gradient. But why? Before drawing any graphs, you must consider what the equation that relates the parameters in question is. In our case, the equation is  v = u + a . t , where v = final velocity, u = initial velocity, a = acceleration due to gravity, and t = time.

But, as we do not supply any initial velocity to the object, u = 0. So the equation becomes  v = a . t 
And since a = acceleration due to gravity, it's value is 9.81ms^-2
Therefore, our final equation becomes  v = 9.81 * t 

This equation can be compared with  y = mx + c  where, c = 0. Now m = 9.81, which must be the gradient of the graph.

Velocity vs Time Graph For Free Fall

Hence, velocity vs time graph for free fall is a straight line with following properties:

• Passes through origin. Why? Because if you compare  v = 9.81 * t  with  y = mx + c , you'll find that c = 0, which is the y-intercept. If a line has y-intercept of 0, it must go through origin.
• Has a gradient of 9.81, Why? Again if you compare  v = 9.81 * t  with  y = mx + c , you'll find that m has a value of 9.81, which is the slope of a straight line.