Class 11 Physics simulations · Motion in a Straight Line

Average vs instantaneous velocity

Shrink the time interval and watch the secant slope approach the tangent slope on the x–t graph.

Open the simulation

What to notice

For uniform acceleration the average over [t₁, t₁+Δt] equals the instantaneous velocity at the interval midpoint.

Key relation

v̄ = Δx/Δt → v = dx/dt as Δt → 0

Try this

Make Δt very small. How close do the two velocities get?

What you can change

• Initial velocity u: 0 to 10 m/s
• Acceleration a: -2 to 4 m/s²
• Start time t₁: 0 to 5 s
• Interval Δt: 0.1 to 4 s

More in Motion in a Straight Line

• Reaction and braking distance
• The catch-up problem
• Motion in one dimension
• Rain and the tilted umbrella
• Relative velocity
• Vertical throw and the turning point
• Area under a v–t graph

See all Class 11 Physics simulations or every Physica simulation.