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pshichka [43]
3 years ago
10

ASAP! I NEED THIS DONE AS QUICKLY AS POSSIBLE WITH WORKING OUT

Mathematics
1 answer:
Elza [17]3 years ago
6 0

Answer:

See explanation.

Step-by-step explanation:

Let us first analyze some principle theory. By definition we know that the velocity ( v ) is a function of a distance  ( d ) covered in some time  ( t ), whilst acceleration ( a ) is the velocity achieved in some time. These can also been expressed as:

v = \frac{d}{t}\\ and a=\frac{v}{t}

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 i-j ) as:

r=(3t^3-t+3)i+(2t^2+2t-1)j         Eqn.(1)

Let us solve.

<u>Part (a) Velocity: </u><u>we need to differentiate Eqn.(1) with respect to time as:</u>

v(t)=\frac{dr}{dt}\\\\ v(t)=[(3)3t^2-1]i+[(2)2t+2]j\\\\v(t)=(9t^2-1)i+(4t+2)j            Eqn.(2)

<u>Part (b) Acceleration: </u><u>we need to differentiate Eqn.(2) with respect to time as:</u>

<u />a(t)=\frac{dv}{dt}\\ \\a(t)=[(2)9t]i+4j\\\\a(t)=(18t)i+4j<u />

<u />

Thus the expressions for the velocity and the acceleration of particle P in terms of t are

v(t)=(9t^2-1)i+(4t+2)j   and   a(t)=(18t)i+4j

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