Question

the velocity of an object is given as v=2t +3t^3. what is the acceleration of the object at t=2s ?

Answer 1

Answer:

The velocity of an object is given as $v = 2t+3t^3$  the acceleration of the object at t=2s will be $38\ m/s^2$

Step-by-step 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 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,

        $v = 2t+3t^3$               $t = 2s$

       Taking the derivative of v,

       $a=\frac{d v}{d t}= 2+9t^2$

       At $t = 2s$

       $a= 2+(9\times 2^2)= 38\ m/s^2$