A motorcycle is travelling along a straight road at 8 m/s. It accelerates at 1m/s2 for a distance of 18 m. Calculate the time it has taken to cover 18 m.      Please answer this .....

Solution-

Given Values:

s (distance traveled) = 18 m
u (initial velocity) = 8 m/sec
a (acceleration) = 1 m/sec²
t (time) = To be calculated

Now, using the second equation of motion;

$$\begin{gathered} \mathrm{s}=\mathrm{ut} + \frac{1}{2}{\mathrm{at}}^2 \\ 18=8\left(\mathrm{t}\right) + \frac{1}{2}\left(1\right){\mathrm{t}}^2 \\ 18=8\mathrm{t} + 0.5{\mathrm{t}}^2 \\ -8\mathrm{t} - 0.5{\mathrm{t}}^2+18=0 \\ \mathrm{Taking} \mathrm{negative} \mathrm{of} \mathrm{both} \mathrm{the} \mathrm{sides}, \\ 8\mathrm{t} + 0.5{\mathrm{t}}^2-18=0 \\ \mathrm{On} \mathrm{solving} \mathrm{the} \mathrm{quadratic} \mathrm{equation}, \mathrm{we} \mathrm{get}, \\ \mathrm{t}=\mathbf{2} \mathrm{or} \mathbf{-}\mathbf{18}\mathbf{ }\mathbf{seconds} \end{gathered}$$

Now, we know that time cannot be a negative value. Hence, the final answer will be 2 seconds.