Answer:
See explanation.
Step-by-step explanation:
Let us first analyze some principle theory. By definition we know that the velocity ( ) is a function of a distance (
) covered in some time (
), whilst acceleration (
) is the velocity achieved in some time. These can also been expressed as:
and
We also know that both velocity and acceleration are vectors (therefore they are characterized by both a magnitude and a direction). Finally we know that given a position vector we can find the <u>velocity and the acceleration</u>, by differentiating the vector with respect to time, once and twice, respectively.
Let us now solve our problem. Here we are givine the Position vector of a particle P (in two dimensional space of ) as:
Eqn.(1)
Let us solve.
<u>Part (a) Velocity: </u><u>we need to differentiate Eqn.(1) with respect to time as:</u>
Eqn.(2)
<u>Part (b) Acceleration: </u><u>we need to differentiate Eqn.(2) with respect to time as:</u>
<u /><u />
<u />
Thus the expressions for the velocity and the acceleration of particle P in terms of t are
and