Select kinematic equations and test when a uniform-acceleration model is appropriate.
Method and worked examples
For constant acceleration use v=u+ at, s=ut+ ½at2 and v2=u2+2as. Here u and v are initial and final velocity, s is signed displacement and t is elapsed time. Average velocity is 2u+v only for constant acceleration. Choose a positive direction before substituting.
Near Earth, free fall with negligible air resistance has approximately constant downward acceleration g=9.8m/s2. Taking upward as positive gives a=−9.8m/s2 during ascent and descent. At the highest point velocity is zero but acceleration remains downward. Large drag invalidates the gravity-only constant-acceleration approximation. Check that the chosen equation has the required unknown and compatible units.
Example 1
A cart starts at 3.0m/s and accelerates at 2.0m/s2 for 4.0s. Find velocity and displacement.
v=u+at=3+2×4=11m/s. s=ut+ ½at2=3×4+0.5×2×16=28m.
Example 2
Throw a ball upwards at 14.0m/s. Ignore drag and use g=9.8m/s2. Find its maximum height above release.
Up is positive, so u=+14.0m/s,v=0,a=−9.8m/s2. s=2av2−u2=−19.6−196=10.0m.
Watch out:Only its vertical velocity is zero at that instant. Gravity continues to produce downward acceleration.
3. Constant acceleration and free fall | Year 11 Physics | Ascent Arcade