Question

which option is correct and why​

Answer 1

Answer:

The answer is 3) 25.6m

Explanation:

Here,

$k = \sqrt{2} (m \frac{1}{2} s \frac{ - 5}{2} )$

Here, m is the meter.

S is the second.

Now put the value of k in the velocity – time relation.

$v = ( \sqrt{2} {)}^{2} \: t \frac{3}{2}$

It gives,

$v = 2t \frac{3}{2}$

As we know,

$v = \frac{ds}{dt}$

Now, evaluate the value of, velocity.

$\frac{ds}{dt} = 2t \frac{3}{2}$

Now, separate the variables and integrate the time from 0 to 4 to find the value of distance.

$∫ds = {∫{0}^{} }^{4} \: \: 2t \frac{3}{2} dt$After integration, we get,

$s = 2 | \frac{t \frac{5}{2} }{ \frac{5}{2} } |$

Now put the limits and then

$s = \frac{4}{5} \times 4 \frac{5}{2}$

We get the value of distance,

$s = 25.6m$

Therefore, The distance traversed in 4 seconds is 25.6m