Question

Find acceleration of the object if velocity is given by v = (5t2 + 3t) m/s after t = 5seconds.  ​

Answer 1

Answer:

a=v/t

a=5t²+3t/5

a=5(5)²+3(5)/5

a=125+15/5

a=140/5

a=28ms-²

Answer 2

Answer:

The acceleration of an object if velocity is given by $v = 5t^2+3t$after t = 5 seconds will be $53\ m/s^2$  

Explanation:

         

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

        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,

       Velocity, $v = 5t^2+3t$         Time, $t= 5s$  

• Taking the derivative of v,

       $a=\frac{d v}{d t}= 10t+3$

       At time $t= 5s$

       $a= (10\times5)+3=53 m/s^2$