Question

If the particle has a velocity of 5 m/s along x-axis at origin , where it will be located at t=6 s

Answer 1

Please find below the answer

Answer 2

Acceleration ‘a’ is given by a = 2t +1,

We know acceleration a is $\frac { dv }{ dt }$.

So we can say 2t +1 = $\frac { dv }{ dt }$.

On integrating both sides, we will get,

                                 ${ t }^{ 2 }+t=v-5$

                                 ${ t }^{ 2 }+t+5=v$

Now we know velocity is $\frac { dx }{ dt }$.

So, ${ t }^{ 2 }+t+5=\frac { dx }{ dt }$

On integrating both sides, we get,

                                  $X=\frac { t^{ 3 } }{ 3 } +\frac { t^{ 2 } }{ 2 } +5t$

[substitute value of t to find value of x]

So, x at t= 6s will be

                                   $\frac { 6^{ 3 } }{ 3 } +\frac { 6^{ 2 } }{ 2 } +5\times 6=120m$