A problem using Newton's Second Law of Motion

Question

A 4.00-kg object has a velocity of 3.00i m/s at one instant. Eight seconds later, its velocity has increased to (8.00i + 10.0j) m/s. Assuming the object was subject to a constant total force, find (a) the components of the force and (b) its magnitude.

Answer 1

Constant force means constant acceleration (F = ma). In the x-direction (i), the object went from 3 m/s to 8 m/s in 8 seconds so a_i = (8 - 3)/8 = 0.625 m/s². In the y-direction (j), the object went from 0 m/s to 10 m/s in 8 seconds so a_j = (10 - 0)/8 = 1.25 m/s²

Since F = ma then F_i = ma_i = (4.00)(0.625) = 2.50i N and F_j = ma_j = (4.00)(1.25) = 5.00j N

The magnitude is found using the Pythagorean Theorem: F = √(2.50² + 5.00²) = 5.59 N