A particle is moving in one dimension, its displacement – time relation is given as s = (2t² + 5) where s is in meters and t is in seconds. Find its velocity (in m/s) at t = 1 second.

The correct answer is 4.

To find the velocity of the particle from its displacement-time relation, we use the definition of instantaneous velocity. The instantaneous velocity, $v$, is defined as the rate of change of displacement, $s$, with respect to time, $t$. Mathematically, this is the first derivative of displacement with respect to time:
$v=\frac{ds}{dt}$

The given displacement-time relation is:
$s=2t^2+5$

Now, differentiate $s$ with respect to $t$:
$v=\frac{d}{dt}\left(2t^2+5\right)$

Using the power rule of differentiation, $\frac{d}{dt}\left(t^n\right)=n{t}^{n-1}$, and knowing that the derivative of a constant is zero, we get:
$v=2\cdot \left(2t\right)+0$
$v=4t$

To find the velocity at the specific time $t=1$ second, substitute $t=1$ into the velocity equation:
$v=4\cdot 1=4\text{m/s}$

Thus, the velocity of the particle at $t=1$ second is 4 m/s.