A trolley while going down an inclined plane and starting from rest has an acceleration of $2cm{{s}^{-1}}$. What will be its velocity 3 s after that start?
(a). $6cm{{s}^{-1}}$
(b). $18cm{{s}^{-1}}$
(c). $12cm{{s}^{-1}}$
(d). $10cm{{s}^{-1}}$

- Hint: Use the equation of motion $v=u+at$ ,where ‘u’ is the initial velocity of the body, ‘v’ is the final velocity, ‘a’ is the acceleration of the body and ‘t’ is the given time.

Complete step-by-step solution -

It is said that the body(trolley) is in motion on an inclined plane with an acceleration of $2cm{{s}^{-1}}$. The body is in a straight line motion with constant acceleration. We know that acceleration is the change in velocity per unit time. It tells us by how much the velocity is increasing or decreasing in each second of time. Whether the velocity is increasing or decreasing , depends on the value of the acceleration. If the value of the acceleration of the given body is positive that means the velocity of the body is increasing with time. If the acceleration is negative, that means the velocity of the body is decreasing with time.
So, $\text{acceleration=}\dfrac{\text{change in velocity}}{\text{time taken}}$
If a body is in straight line motion with constant acceleration, change in velocity will simply be the difference in the final velocity and the initial velocity of the body in that given time.
Therefore, $a=\dfrac{v-u}{t}$ ……..(1), where a is the constant acceleration of the body, v is the final velocity, u is the initial velocity and t is the given time.
Now, we can write equation (1) as, ………(2) and with this we can find the velocity of the trolley after 3 seconds.
Put the given values of u, a, t in equation (2).
$\Rightarrow v=0+(2.3)=6cm{{s}^{-1}}$Therefore, the velocity of the trolley moving down the inclined plane after 3 seconds will be $6cm{{s}^{-1}}$.
Hence, the correct option is (a).

Note: The equation (2) only works if the acceleration is constant and the body is motion along a straight line. If the body is not in a straight line motion then we would have to deal the case with vectors.