Physics, asked by sahilrmandhare4162, 1 year ago

The velocity-time relation of a particle starting from rest is given by v = kt
where k = 2 m/s.The distance travelled in 3 sec is ......​

Answers

Answered by ShivamKashyap08
14

\huge{\bold{\underline{\underline{....Answer....}}}}

\huge{\bold{\underline{Given:-}}}

\large{\bold{v = kt}}

k = 2 m/s.

\huge{\bold{\underline{Explanation:-}}}

As velocity is given and we need to find distance we need to integrate it.

so,

\large{\bold{v = \frac{ds}{dt}}}

\large{ds = v.dt}

Integrating

\large{ \implies \displaystyle\int ds = \displaystyle\int v.dt}

Applying limits.

\large{ \implies \displaystyle\int^s_0 ds = \displaystyle\int^3_0 v.dt}

Substituting the value of velocity.

\large{ \implies \displaystyle\int^s_0 ds = \displaystyle\int^3_0 kt.dt}

Now,

\large{ \implies S = \left| \frac{Kt^2}{2} \right|^3_0}

\large{ \implies S = \left| \frac{2 \times t^2}{2} \right|^3_0}

As K value is 2 m/s.

\large{ \implies S = \left| \frac{ \cancel{2}t^2}{ \cancel{2}} \right|^3_0}

Now,

\large{ \implies S \left|t^2\right|^3_0}

\large{ \implies S = (3)^2}

\huge{\boxed{\boxed{S = 9 \: meters}}}

So,the distance travelled in 3 seconds is 90 meters.

Similar questions