### Acceleration Due To Gravity

When a projectile is in the air, under ideal conditions, it accelerates at 9.8 m/s² down.  Because of this the velocity changes by 9.8 meters per second every second in a downward direction. So watch how the 9.8 m/s² down never changes but the velocity constantly does because of it.

Note: Many classes use 10 m/s2 down because it is 9.8 m/s2 down rounded and is easier to conceptualize.  So continue to use what your teacher tells you to.

### Acceleration Equation Variables

 Name Variable Unit Unit Abbreviation Initial Velocity or Initial Speed vi or viy meters per second m/s Final Velocity or Final Speed vf or vfy meters per second m/s Time t seconds s Acceleration a or g (g) acceleraton due to gravity 9.8 m/s2 down on earth meters per second squared m/s2 Displacement or Distance X or Y (X): X axis displacement (Y): Y axis displacement meters m

Subscripts describing to variables above: initial(i), Y axis(y),  final(f),  initial Y axis(iy),  final Y axis(fy)

Note:

• In my example below,  we use a for acceleration due to gravity and x for displacement.  This way we can use the generic acceleration equations from the equation sheet.  Many classes make you memorize your equations so it's best to just use the original.
• Specialized equations seen in the picture have a as g (acceleration due to gravity) and x as y.  A falling object's displacement is down, the reason for the negative sign.
• The equations to the right all are three of the four original acceleration equations in the last section.  The one missing does not have acceleration as a variable.

### Working Through an Acceleration Due to Gravity (Freefall Problem)

When you read a problem that has an object thrown, dropped, or rolled off a table the object will be in freefall. Freefall does not mean it fell to get in the air but is only under the influence of gravity.  In later units we will encounter air resistance but unless you are told otherwise assume an ideal condition with no air resistance.  When you read a problem and the object is in the air as a projectile (just under the influence of gravity), the acceleration will be 9.8 m/s2 down.

### Example Acceleration Due to Gravity Question:

Jose dropped a ball from a height of 15m from rest, how fast was it going before it hit the ground?

• Step one: read the entire problem and determine if an object is in the air (and not being propelled like a rocket), if only being affected by gravity a=10 m/s2 down should be part of your givens list.
• Step two: pick out the unknown the question is asking you to solve for and add it to a givens list.  (example: vf = ?)
• Step three: pick out the variables given in the equation. (example: vi = 0, x= falls 10 down (or -10 m) a= -9.8 m/s2)
• Step four: figure out which variable is missing (example: t is missing)
• Step five: pick the one equation that does not have that missing variable (in this example: vf2 = vi2 + 2ax)

### Example Problems

How fast is a ball moving when falling from rest and hits the ground 1.5 seconds later?

• Note: since all of the givens are scalars or in no direction, I will call down positive and a positive final answer on a vector gets the direction down

Givens

• vi = 0 m/s
• a = 9.8 m/s2 down
• t = 1.5 s
• vf = ?

Equation:

• vf = vi + at

Work:

• vf = 0 + (9.8)(1.5)
• vf = 14.7 m/s down

What is the displacement of a ball that is thrown up at 15 m/s one second after thrown?

• Note: There is an up direction and a down in this example so I call up positive and down negative.  A positive answer on a vector comes with the direction up.

Givens

• x = ?
• vi = 15 m/s up = + 15 m/s
• t = 1 s
• a = 9.8 m/s2 down = - 10 m/s2

Equation

• x = vit + at2

Work

• x = (15)(1) + (-9.8)(12)
• x = +5 m = 5.2 m up

### What a Constant Acceleration of 10m/s2 Down Does to Velocity

Observe the two animations below of a = 10 m/s2 down or changing velocity by 10 m/s down every second.  The one on the left is of a ball thrown up at 10m/s, the next dropped from rest, and the last thrown down at 10 m/s.  On the right you see a ball dropped and another thrown down at 10 m/s.  The ball on the right is always going faster down and therefore covers more meters per second.  Notice how the two keep on getting further apart.

### Acceleration Due to Gravity Quiz

Acceleration Due to Gravity Quiz

Do you know what an acceleration due to gravity of 9.8 m/s2 really means?

Find out by taking our acceleration due to gravity quiz

1 / 9

What is the final velocity of a ball throw down at 10 m/s after two seconds?

2 / 9

What is the displacement of a ball thrown up at 25 m/s after 4 seconds in the air? (Note the ball can be below the ground)

3 / 9

When a ball is thrown in the air straight up, what is the velocity at the top of its flight?

4 / 9

When a ball is thrown in the air straight up, what is the acceleration at the top of its flight?

5 / 9

When a ball is thrown in the air straight up, what is the acceleration if still in the air after 2 seconds of its flight?

6 / 9

One ball is thrown up and another is dropped.  Which ball will have a greater acceleration after 2 seconds?

7 / 9

One ball is thrown up and another is dropped.  Which ball will have a greater downward velocity after 2 seconds?

8 / 9

One ball is thrown down at 5 m/s and another is thrown down at 10 m/s at the same time.  How will the distance between them change as they fall.

9 / 9

A 0.5 kg rock and a 150 kg boulder were dropped from a cliff 65 meters high.  Which one would hit the ground first ignoring air resistance?