Question

A body of mass 5kg under the action of constant force \[\vec F = {F_x}\hat i + {F_y}\hat j\] has velocity at \[t = 0s\] as \[\vec v = (6\hat i - 2\hat j)m/s\] and at \[t = 10s\] as \[\vec v = + 6\hat j{\text{ }}m/s.\] The force \[\vec F\] is:
A.) \[( - 3\hat i + 4\hat j)N\]
B.) \[( - \dfrac{3}{5}\hat i + \dfrac{4}{5}\hat j)N\]
C.) \[(3\hat i - 4\hat j)N\]
D.) \[(\dfrac{3}{5}\hat i - \dfrac{4}{5}\hat j)N\]

Answer 1

Hint: A force is a push or pull on an object which results from the interaction of the object with another object. Whenever the two objects touch, there is a force on each of the objects. Once the contract ends, the two subjects do not feel forced any more. Forces exist only by interaction.

Complete step-by-step answer:
Formula Used: \[F = \dfrac{{dP}}{{dt}}\]

Given in the question:

\[{\vec v_i} = (6\hat i - 2\hat j)m/s\] at \[t = 0\sec \]
\[{\vec v_j} = 6\hat jm/s\] at \[t = 10\sec \]

m = 5kg

Constant force, \[F = \dfrac{{dP}}{{dt}}\]

\[F = m\dfrac{{dv}}{{dt}}\]
\[F = 5\dfrac{{{{\vec v}_f} - {{\vec v}_i}}}{{{t_f} - {t_i}}}\]
\[F = 5\dfrac{{(6\hat j) - (6\hat i - 2\hat j)}}{{10}}\]
\[F = \dfrac{{ - 6\hat j + 8\hat j}}{2}\]
\[F = ( - 3\hat i + 4\hat j)\].

Hence, option A is the right answer.

Note: Constant Force is a quick tool to add constant strength to a Rigid Body. It works great for one shot objects like rockets, because you don't want it to start with a major velocity but rather to accelerate. Motion of an object on the earth's surface subject to the pull of the gravity of the earth is an example of such a system with such energy.