Starting from the origin at time t = 0, with initial velocity 5ĵ ms⁻¹ , a particle moves in the x-y plane with a constant acceleration of ( 10î + 4ĵ ) ms⁻². At time t, its coordinates are (20 m, y₀ m). The values of t and y₀ are, respectively:

Solution

Physics sir · 3 steps

Split the motion into x and y: the x-direction has no initial speed, so it gives you t straight away.

1. Split the motion. The acceleration is constant, so s = ut + 1/2at² works separately along x and along y. Along x: uₓ = 0, aₓ = 10 m s⁻². Along y: u_y = 5 m s⁻¹, a_y = 4 m s⁻².
2. Find t from x. 20 = 0 × t + 1/2 × 10 × t² = 5t², so t² = 4 and t = 2 s.

   y₀ = u_y t + 1/2a_y t² = 5 × 2 + 1/2 × 4 × 2² = 10 + 8 = 18 m

3. So. t = 2 s and y₀ = 18 m, which is option (b).

The idea to keep. In 2D motion with constant acceleration, treat x and y as two separate 1D problems joined only by the same time t. Find t from the simpler direction first.

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