(Instantaneous) velocity and speed

The instantaneous velocity or simply velocity v(t) of a particle at time t is the slope of the curve x(t) at t.

The instantaneous speed or simply speed of a particle at time t is the magnitude of its velocity at t.

velocity is a vector and speed is a scalar

Question:

Suppose a particle has an x(t) curve shown below. Determine the sign of the
velocity at t_{A}, t_{B} and t_{C}.

Question:

The following plot describes
the position of a particle as a function of time. Find the velocity and
speed of the particle at t=-2.5, -1.0, 0, 1.0 and 1.5 sec.

Question:

Find the velocity of the particle which follows the
following curves (x in m and t in sec):

(a)
x_{1}(t) = 100 + 4 t.

(b) x_{2}(t)
= 3 + 4 t.

Question:

If you are given a particle velocity v(t), can you
find the position of the particle x(t)?

Question:

If a particle has velocity v(t) = 8 m/sec. What is
its position x(t) for the following to cases

(a) x(t = 10
sec) = 100 m?

(b) x(t = 10
sec) = 5 m?

Question:

If a particle has velocity v(t) = v_{0} + a
t, where v_{0} and a are constant and x(t=0) = x_{0}. What is
its position x(t)?

Graphical Summary

Here x(0)=x_{0},
v(0) = v_{0} and a is a constant