8
Velocity in non-uniform motion
Textbook: pp. 34–36
GoalKnow non-uniform motion, average velocity and instantaneous velocity.
New words
non-uniform motion · notekis harakataverage velocity · o‘rtacha tezlikinstantaneous velocity · oniy tezliktotal path · butun yo‘l
Explanation
Motion in which unequal paths are covered in equal time intervals is called non-uniform motion. The velocity keeps changing. The ratio of the total path covered to the total time taken is the average velocity: υ_avg = s/t. It is not the simple arithmetic mean of velocities, since the body may have travelled at different velocities for different times. The velocity of a body at a given instant is its instantaneous velocity; a car’s speedometer shows exactly this.
Worked examples
A car covers 100 km in the first 2 h and 140 km in the next 3 h. υ_avg = (100 + 140) : (2 + 3) = 240 : 5 = 48 km/h.
A pupil walks half the way at 4 m/s and the rest at 6 m/s. The average is not (4 + 6) : 2 = 5 m/s: for a 120 m route the time is 60 : 4 + 60 : 6 = 15 + 10 = 25 s, so υ_avg = 120 : 25 = 4.8 m/s.
Class activity
“Speedometer watch”: the teacher shows a picture or video of a speedometer; pupils note how the speed changes and identify instantaneous velocity. Safety: never distract a driver.
Practice
1
How is average velocity found?
Divide the whole path by the whole time: υ_avg = s/t.
2
A body covers 60 m in 10 s and the next 90 m in 20 s. Average velocity (m/s)?
5
3
What is instantaneous velocity and which instrument shows it?
The velocity at a given instant; the speedometer shows it.
4
Why is average velocity not just the arithmetic mean of the velocities?
Because the body moves at different velocities for different times; only the total path and total time count.