Question

position is given by x (t)=5t^2+3t + 6.find the velocity at t=2s​

Answer 1

Answer:

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Answer 2

Answer:

The position is given by $x=5t^2+3 t+6$ the velocity at t=2s​ is, $23m/s$

Explanation:

• The velocity can be defined as the rate of change of position with respect to time and

• in the same way, acceleration can be defined as the rate of change of velocity or the second derivative of position with respect to time.

• Let t be the time, x be the position, v be the velocity and a be the acceleration of an object.

        Then, by definition,

        $\mathrm{v}=\frac{\mathrm{dx}}{\mathrm{d} t}$

        and

        $a=\frac{d v}{d t}$    

• In the question, it is given that,

       $x=5t^2+3 t+6$       $t= 2s$          

 

• Taking the derivative of x,

      $v=\frac{d (5t^2+3t+6 ) }{d t}= 10t+3$

      put $t=2s$

       $v = (10\times 2) +3$

           $=23m/s$