Question

A trolley, while going down an inclined plane, has an acceleration of $2{\text{ }}cm{\text{ }}s{\;^{ - 2}}$. What will be its velocity $3{\text{ }}s$ after the start?

Answer 1

Newton’s equations of motion are equations that can define the manners of a physical system in terms of its motion with the help of time as a function. Using the equation of motion we can get the velocity of the trolley after the given time.

Complete answer:
From the question, we can say that
Initial velocity $\left( u \right){\text{ }} = {\text{ }}0$(as the trolley starts from the rest position)
Acceleration $\left( a \right) = {\text{ }}0.02{\text{ }}m{s^{ - 2}}$
Time $\left( t \right){\text{ }} = {\text{ }}3s$
To find out the velocity,$3{\text{ }}s$ after the start
From the first motion equation, $v = u + at$
Therefore, the final velocity of the trolley
$\left( v \right){\text{ }} = {\text{ }}0{\text{ }} + {\text{ }}\left( {0.02{\text{ }}m{s^{ - 2}}} \right)\left( {3s} \right) = {\text{ }}0.06{\text{ }}m{s^{ - 2}}$Therefore, the velocity of the trolley after $3{\text{ }}s$is$6{\text{ }}cm{s^{ - 2}}$

Note:
Newton’s equation of motion can be given as
$F = \dfrac{{dp}}{{dt}} = m\dfrac{{dv}}{{dt}} = m\dfrac{{d{r^2}}}{{d{t^2}}}$
An explanation of the motion of a particle needs a result of the second-order differential equation of motion. This equation of motion is integrated to find $r\left( t \right)\;$and, $v\left( t \right)$, if the primary conditions and the force field $F\left( t \right)$are identified. Results of the equation of motion can be complex for various practical examples, but there are numerous methods to simplify the solution.