A force F⃗ = (40î + 10ĵ)N acts on a body of mass 5 kg. If the body starts from rest, its position vector r⃗ at time t = 10 s, will be :

Solution

Physics sir · 4 steps

Find the acceleration vector first, then use s = 1/2at² on each component separately.

1. Acceleration. By Newton's second law, a⃗ = F⃗ / m = (40î + 10ĵ)/5 = (8î + 2ĵ) m s⁻². The force is constant, so this acceleration stays the same at all times.
2. Start from rest. The body starts at rest, so u⃗ = 0. Take the starting point as the origin, so the displacement is the position vector.

   r⃗ = 1/2a⃗ t² = 1/2(8î + 2ĵ)(10)²

3. Put in numbers. 1/2 × 100 = 50, so r⃗ = 50 × (8î + 2ĵ) = (400î + 100ĵ) m.
4. So. The position vector at t = 10 s is (400î + 100ĵ) m, which is option (c).

The idea to keep. A constant force gives a constant acceleration vector. Treat the x and y directions as two separate straight-line problems, then put the components back together.

Answer from the NTA final answer key. Solution by PrepWiser.