Question

what does velocity describe?
what shows the speed on a distance-time graph?
what is the difference between average speed and instantaneous speed?
How can two or more velocities be combined?

Answer 1

1) What does velocity describe?
- Velocity is a vector quantity that describes how fast and in what direction an object’s position changes.
- Mathematically: v = Δs / Δt (average velocity) or v(t) = ds/dt (instantaneous velocity), where s is displacement.

2) What shows the speed on a distance–time graph?
- The speed (magnitude of velocity) is the gradient (slope) of the distance–time curve: speed = change in distance / change in time = Δd/Δt.
- On a straight line the slope is constant (constant speed). A steeper line = higher speed. If the graph is distance (always positive) the sign/direction is not shown; on a displacement–time graph the slope gives signed velocity.

3) Difference between average speed and instantaneous speed
- Average speed = total distance traveled / total time taken. It is a single value over an interval.
Example: 150 km in 3 h → average speed = 50 km/h.
- Instantaneous speed = speed at a specific moment (the limit of average speed over an infinitesimal time interval). On a displacement–time graph it is the magnitude of the slope of the tangent at that time (instantaneous velocity is the signed slope).

4) How can two or more velocities be combined?
- Velocities are vectors, so combine them by vector addition.
- Colinear (same line): add algebraically, taking direction signs into account (e.g., +5 m/s and −2 m/s → +3 m/s).
- General case: use head-to-tail (graphical) or component method:
- Resolve each velocity into components (vx, vy), sum components: Vx = Σvx, Vy = Σvy.
- Resultant magnitude |V| = sqrt(Vx^2 + Vy^2), direction θ = arctan(Vy / Vx).
- For perpendicular example: 3 m/s east and 4 m/s north → resultant 5 m/s at arctan(4/3) ≈ 53.1° north of east.
- Also note relative velocity: v_AB = v_A − v_B (velocity of A relative to B).