10
Velocity of uniformly variable motion
Textbook: pp. 40–43
GoalApply υ = υ₀ + at; describe the velocity graph in words.
New words
velocity formula · tezlik formulasiinitial velocity · υ₀acceleration a · tezlanish avelocity graph · tezlik grafigi
Explanation
From a = (υ − υ₀)/t we find the velocity after time t: υ = υ₀ + at. If a body starts from rest (υ₀ = 0) the formula becomes υ = at. If the acceleration is opposite to the velocity, a is taken as negative: υ = υ₀ − |a|t. The velocity–time graph is then a slanted straight line: for speeding-up motion it rises, for slowing-down motion it falls. The steeper the graph, the larger the acceleration. When the velocity reaches 0, the body stops.
Worked examples
A car at rest accelerating at 2 m/s² for 8 s reaches υ = at = 2 · 8 = 16 m/s.
A bicycle at υ₀ = 10 m/s slowing with a = −0.5 m/s² has, after 10 s, υ = 10 − 0.5 · 10 = 5 m/s.
Class activity
“Graph game”: the teacher describes a velocity graph in words (“from rest, +2 m/s every second”); pupils write the velocities for 0, 1, 2, 3 s. Safety: use no sharp tools.
Practice
1
Write the velocity formula (constant a).
υ = υ₀ + at.
2
A body starting from rest with a = 3 m/s² for 5 s: velocity (m/s)?
15
3
υ₀ = 20 m/s, a = −4 m/s². After how many seconds does the body stop?
5
4
If the velocity graph is a falling slanted line, what is the motion like?
Slowing down: velocity decreases, and acceleration is opposite to velocity.