The distance Y metres covered by a body in t seconds, is given by s = 3t² – 8t + 5. The body will stop after

Correct Option: The correct answer is 4/3 s.

Step-by-Step Explanation:

The distance (displacement) $s$ covered by the body in time $t$ is given by the equation:

$$s=3t^2-8t+5$$

A moving body comes to a stop when its instantaneous velocity ($v$) is equal to zero. Velocity is defined as the rate of change of displacement with respect to time, which can be found by taking the first derivative of the displacement function with respect to $t$:

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

Differentiating the given equation with respect to $t$:

$$v=\frac{d}{dt}(3t^2-8t+5)$$

Using the power rule of differentiation, $\frac{d}{dt}\left(t^n\right)=n{t}^{n-1}$, we obtain:

$$v=3\left(2t\right)-8\left(1\right)+0$$

$$v=6t-8$$

To find the time when the body stops, set the velocity ($v$) to zero:

$$6t-8=0$$

Now, solve for $t$:

$$6t=8$$

$$t=\frac{8}{6}$$

Simplifying the fraction by dividing the numerator and the denominator by their greatest common divisor (2) gives:

$$t=\frac{4}{3}\text{ s}$$

Therefore, the body will stop after 4/3 s.