Acceleration

When a particle has changed its velocity from position v_{i} to
position v_{f} during the time interval Dt =
t_{f} - t_{i}, its average acceleration
v_{avg }is

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

Question:

If a particle traces
the following equation

x(t) = 10 + 20 t + 5.0 t^{2}

what is its acceleration?

Question:

If a particle has a constant acceleration a(t) = a,
find its velocity v(t) and its position x(t) as a function of time. assume
that v(t=0) = v_{0} and x(t=0) = x_{0}.

Question:

Which of the statements below is correct ?

(a) If the sign of the velocity and acceleration of a particle are the same, the speed of the particle increases. If the sign are opposite, the speed decreases.

(b) Positive acceleration means that the speed of the particle is increasing while negative particle means that the speed decreases.

Graphical Summary