Comparative Study of Instantaneous Speed and Instantaneous Velocity
Instantaneous velocity or simply velocity is defined as rate of change of particle's position with time = where the position of a particle at any instant changes by Δ in a small time Δ t. he magnitude of velocity is called speed i.e. speed = | velocity | i.e. v = | |
Note : In straight line motion there is no change in direction so and v both have same meaning.
Note :
(a) Velocity is a vector while speed is a scalar having same units (m/s) and dimension [LT^–1]
(b) If during motion velocity remains constant throughout a given interval of time, the motion is said to be uniform and for uniform motion, = constant =
However converse may or may not be true i.e. If = , the motion may or may not be uniform.
(c) If velocity is constant, speed ( = | velocity |) will also be constant. However conversdree may or may not be true i.e. if speed = constant, velocity may or may not be constant as velocity has a direction in addition to magnitude which may or may not change. e.g. in case of uniform rectilinear motion. = constant and so speed || = constant while in case of uniform circular motion, v = constant but ≠ constant due to change in direction.
(d) Velocity can be positive or negative, as it is a vector but speed can never be negative as it is the magnitude of velocity i.e. v = ||
(e) If displacement is given as a function of time, the time derivative of displacement will give velocity and modulus of velocity gives speed.
e.g. s = A₀ – A₁t + A₂t², v = = – A₁ + 2A₂t. So, initially (t = 0), velocity = – A₁, while speed = |–A₁| = A₁
Special Note : It is common misconception, that Which is totally different from the above value of .
(f) As by definition, v = , the slope of displacement versus time graph gives velocity.

i.e. v = = tan θ = slope of s-t curve
(g) As, v = ⇒ ds = vdt
From figure vdt = dA. so, dA = ds
∴

Area under velocity versus time graph with proper algebraic sign gives displacement while without sign gives distance.

e.g. From the adjoining v-t graph.
The distance travelled by body in time t₃ = Area I + Area II + Area III and the displacement of body = Area II – Area III – Area I