Key relationship
vavg = Δx/Δt; speedavg = distance/Δt; v(t) = dx/dt
Physics · Class 11
Average & instantaneous
The secant joining two positions gives average velocity over that interval. The tangent at the current time gives instantaneous velocity. Speed is the magnitude of instantaneous velocity, while average speed uses the full distance travelled. A varying acceleration makes the distinction between a secant and tangent visible.
Open the interactive experiment →A graph slope can describe an interval or an instant.
இரு நிலைகளை இணைக்கும் கோட்டின் சாய்வு சராசரி திசைவேகம். ஒரு நேரத்தில் உள்ள தொடுகோட்டின் சாய்வு உடனடி திசைவேகம். சராசரி வேகம் கடந்த மொத்தத் தொலைவைப் பயன்படுத்தும்.
Key notes, relationships and model limits
Remember
The secant joining two positions gives average velocity over that interval. The tangent at the current time gives instantaneous velocity. Speed is the magnitude of instantaneous velocity, while average speed uses the full distance travelled. A varying acceleration makes the distinction between a secant and tangent visible.
Common trap
Average speed need not equal the magnitude of average velocity when direction changes.
Model limits
Smooth analytic route x = ut + ½at² + ⅙jt³, x0 = 0; j is a constant acceleration-change rate. The centred interval is clipped at 0 and 10 s. Distance is integrated exactly across reversals.
What you will learn
Read secant and tangent slopes; compare speed with velocity; examine the small-interval limit.
Try the experiment
Select a time, widen the interval, then shrink it. Try the reversal preset and compare both averages.
Think of it this way
A trip average describes the whole interval; a speedometer describes what happens now.
Worked example
For x = t³/6, v = t²/2. At t = 2 s the tangent slope is 2 m/s. The secant from 1 to 3 s has slope (27/6 − 1/6)/2 = 13/6 m/s.
Why this matters
A measurement over an interval and a local rate answer different questions.
Before you start
Signed numbers · coordinates · gradients · area under a graph
Check your understanding
An object travels +4 m, then −4 m in 4 s. What are its average speed and average velocity?
- 0 m/s and 2 m/s
- 2 m/s and 0 m/s
- Both are 0 m/s
Read the explanation
Distance is 8 m, giving average speed 2 m/s. Displacement is zero, giving average velocity zero.
Course connection: CBSE XI Chapter 2; NEET and JEE Main Unit 2; JEE Advanced Mechanics. Check the selected syllabus for relative-velocity scope.