The instantaneous velocity of a freely falling object

In summary, the instantaneous velocity of a freely falling object 10 seconds after being released from a position of rest is 98 m/s. The average velocity during this 10 second interval can be calculated as 49 m/s using the formula v = at, or as 50 m/s using the formula v = (vf+vo)/2. The distance traveled during this time can be calculated as 490 m using the formula d = 1/2 * gt^2, or as 500 m using the formula x = vot + 1/2at^2. All of these equations are interrelated and depend on the acceleration due to gravity, which can be taken as either 9.8 m/s^2 or
  • #1
sammyj
4
0
What is the instantaneous velocity of a freely falling object 10 s after it is released from a position of rest? What is its average velocity during this 10 s interval? How far will it fall during this time?

I had asked a few friends for help and I keep getting mixed answers.

v = gt
98m/s = 9.8m/s * 10
Average V = initial v + final v
2
Average V = 0m/s + 98m/s
2

Average V=49m/s
Distance Traveled d = ½ gt squared
½ * 9.8m/s * 10 squared = 490m

or

Vf=Vo+at = 0msec+10msec2(10sec)= 100msec

AverageVelocity=Vf+Vo2=100ms+0ms2=50msec

X=Vot +12at2=0ms(10sec)+12(10msec2)(10sec)2=500 meters

Who's on the right path?
 
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  • #2
Welcome to PF.

You can approach average velocity either way.

V = a*t => Vavg = 1/2*a*t

or X = 1/2*a*t2

Vavg = Xtot/Ttot = 1/2*a*t2/t = 1/2*a*t

V2 = 2*a*x = 2*a*(1/2*a*t2) = a2t2

V = a*t

They are all interrelated.
 
  • #3
The answers came up slightly different would it matter?
 
  • #4
sammyj said:
The answers came up slightly different would it matter?

There is no difference that I see. Acceleration is due to gravity in both cases.

The bottom equation uses g = 10 instead of 9.8.
 

What is the definition of instantaneous velocity?

The instantaneous velocity of a freely falling object is the rate of change of its position at a specific moment in time. It is a vector quantity that includes both the magnitude and direction of the object's motion.

How is the instantaneous velocity of a freely falling object calculated?

The instantaneous velocity of a freely falling object can be calculated by dividing the change in the object's position by the change in time. This can be represented mathematically as v = ∆x/∆t, where v is the instantaneous velocity, ∆x is the change in position, and ∆t is the change in time.

What factors affect the instantaneous velocity of a freely falling object?

The instantaneous velocity of a freely falling object is affected by two main factors: the gravitational acceleration of the object and the presence of air resistance. Objects with a larger gravitational acceleration (such as those on Earth compared to the moon) will have a higher instantaneous velocity, while objects with a greater amount of air resistance will have a lower instantaneous velocity.

How is the instantaneous velocity of a freely falling object different from average velocity?

Instantaneous velocity and average velocity are both measures of an object's motion, but they are calculated differently. Average velocity is calculated by dividing the total distance traveled by the total time taken, while instantaneous velocity is calculated at a specific moment in time. Average velocity gives an overall picture of an object's motion, while instantaneous velocity provides information about an object's motion at a specific point in time.

Can the instantaneous velocity of a freely falling object ever be negative?

Yes, the instantaneous velocity of a freely falling object can be negative. This occurs when the object is traveling downwards, in the opposite direction of its initial motion. However, the object's average velocity may still be positive if it has a greater velocity when moving upwards than when moving downwards.

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