← Free fall

A dropped object's velocity after a time

A motorcycle moving at 8 m/s accelerates at a constant 3 m/s² for 4 s. Calculate its final velocity, in m/s.

Let go of an object and it is in free fall. A stone dropped from a bridge has been falling for 2 s. How fast is it moving?

You've already seen the free-fall acceleration of 9.8 m/s². Put it into the equation v = v₀ + at, and it tells you how fast a dropped object moves after any number of seconds.

Two facts set up the whole calculation. A dropped object starts from rest, so v₀ = 0. And take down as the positive direction, so a = +9.8 m/s² and the velocity comes out as a positive downward value.

Substitute v₀ = 0, a = 9.8 m/s², and the falling time into v = v₀ + at. The result is the velocity, in m/s, directed downward.

A stone is dropped from a bridge. Air resistance is ignored. How fast is the stone moving 2 s after it is released?

Write down the values in the question:

v₀ = 0 (dropped from rest)

a = 9.8 m/s² (taking down as positive)

t = 2 s

Write down the equation:

v = v₀ + at

Substitute in the values:

v = 0 + 9.8 × 2

Simplify:

v = 19.6 m/s downward

The velocity grows by the same amount every second, because free-fall acceleration means the velocity changes by 9.8 m/s downward with each second of flight.

Sanity check: 9.8 m/s arrives with each second of falling, so twice the time must give twice the velocity.

A rock is dropped from a sea cliff and falls for 4 s. Air resistance is ignored. What is its velocity after those 4 s? Enter the value in m/s; the direction is downward.

A roof tile slips off a tall building and falls for 3.5 s before hitting the ground. Air resistance is ignored. How fast is it moving when it lands?

Write down the values in the question:

v₀ = 0 (the tile slips from rest)

a = 9.8 m/s² (taking down as positive)

t = 3.5 s

Write down the equation:

v = v₀ + at

Substitute in the values:

v = 0 + 9.8 × 3.5

Simplify:

v = 34.3 m/s downward

A set of keys is dropped from an apartment window and falls for 2.5 s. Air resistance is ignored. What is its velocity after those 2.5 s? Enter the value in m/s; the direction is downward.

A supply crate is released from a hovering helicopter and falls for 5 s. Air resistance is ignored. What is its velocity after those 5 s? Enter the value in m/s; the direction is downward.

Your turn

A camera slips out of a hovering drone's mount and falls for 1.5 s before landing in deep snow. Air resistance is ignored. What is its velocity just before landing? Enter the value in m/s; the direction is downward.

A brick is dropped from a crane platform. Air resistance is ignored. How much faster is the brick moving after 6 s of falling than after 4 s of falling? Enter the difference in m/s.

A pebble is dropped into a deep canyon and falls for 4.5 s before hitting the river. Air resistance is ignored. What is its velocity just before it hits? Enter the value in m/s; the direction is downward.