(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 tA, tB and tC.

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)    x1(t) = 100 + 4 t.
(b)    x2(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) = v0 + a t, where v0 and a are constant and x(t=0) = x0. What is its position x(t)?

Graphical Summary

Here x(0)=x0, v(0) = v0 and a is a constant