Vectors

Step 1: The magnitude of a unit vector is 1, so:
Step 2: Solving for , we get:

Step 3: Hence, Therefore, the correct answer is (E).

The area under a force ( ) vs time ( ) graph represents the impulse, which is the change in momentum of an object. However, if the force is constant, the area under the graph would represent the work done, as the force applied over a certain distance (which is related to time) results in work. The equation for work done is: Where is the distance moved by the object, which can be linked to time through the velocity of the object. Thus, the area under the force-time graph represents work done.

Concept:

Step 1: Check range.
For 7 and 2: Thus 4 is not possible.

Concept:

Step 1: Substitute values.


Step 2: Compute.

Concept:
• Dot product:

Step 1: Compute dot product


Step 2: Equate
Final Conclusion: