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  • The position of a particle is given by where t is in seconds (a) Find the v and a of the particle?

Q. 4.20 The position of a particle is given by r=3.0t\; \hat{i}-2.0t^{2}\; \hat{j}+4.0\; \hat{k}\; m where t is in seconds and the coefficients have the proper units for r to be in metres.

(a) Find the v and a of the particle?

Answers (1)

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(a)  We are given the position vector    r=3.0t\; \hat{i}-2.0t^{2}\; \hat{j}+4.0\; \hat{k}\; m

The velocity vector is given by:-  

v \ =\ \frac{dr}{dt}

 v\ =\ \frac{d\left ( 3.0t\; \hat{i}-2.0t^{2}\; \hat{j}+4.0\; \hat{k} \right )}{dt}

or   v\ =\ 3\; \hat{i}-4t\; \hat{j} 

Now for acceleration :

  a \ =\ \frac{dv}{dt}

        =\ d(\frac{3\; \hat{i}-4t\; \hat{j})}{dt}

        =\ -4\; \hat{j}

Posted by

Devendra Khairwa

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