Motion in One Dimension

Free Fall

dropping under gravity

A dropped object is constant acceleration with gravity doing the speeding up. With g = 10 the numbers stay clean.

Example

A dropped object is just constant acceleration with gravity doing the speeding up. With g = 10 the numbers stay clean.

highlighted = computed this step

Set up the drop

A ball is dropped from rest and falls for 2 seconds. We use 10 metres per second squared for gravity to keep the arithmetic clean; the real value is about 9.8 metres per second squared, a little smaller.

g=10 m/s2,t=2 sg = 10\ \text{m}/\text{s}^{2}, \quad t = 2\ \text{s}
A ball at the moment it is droppedA ball held above the floor with a downward arrow showing the pull of gravity.ballg

Speed when it lands

Falling speed is gravity times time: 10 times 2 is 20 metres per second.

v=g t=10 m/s2 ⋅ 2 s=20 m/sv = g\,t = 10\ \text{m}/\text{s}^{2} \,\cdot\, 2\ \text{s} = \hl{20}\ \text{m}/\text{s}

Distance fallen

Free fall is the constant-acceleration distance with gravity for the acceleration: one half times 10 times the time squared, 4.

y=12 g t2=12 ⋅ 10 m/s2 ⋅ 4 my = \tfrac{1}{2}\,g\,t^{2} = \tfrac{1}{2} \,\cdot\, 10\ \text{m}/\text{s}^{2} \,\cdot\, 4\ \text{m}

Compute the fall

The ball falls 20 metres. As with any constant acceleration, equal times give growing gaps.

y=20 my = \hl{20}\ \text{m}
The ball falls in growing stepsA dropped ball shown at each whole second; the gaps grow and the downward velocity arrows lengthen as it speeds up toward the floor.t=0t=1ball
mechanics Free fall reuses the constant-acceleration distance formula with gravity for the acceleration; g = 10 keeps it exact, and the gaps grow as it falls.