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

Hint: 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.