Question

A particle moves along the x-axis so that at any time t≥0 its position is given by x(t)=12(a−t)2, where a is a positive constant. For what values of t is the particle moving to the right? The particle is moving to the right only if 0

Answer 1

The particle moves to the right when 0 ≤ t < a

Step-by-step explanation:

Since at any time t≥0 its position is given by x(t) = 12(a−t)², the particle moves to the right if x(t) > 0

So, x(t) > 0 ⇒ 12(a−t)² > 0 ⇒ (a−t)² > 0

So, (a−t)² > 0

taking square-root of both sides, we have

√(a−t)² > √0

⇒ (a−t) > 0

⇒ a > t

Since t ≥ 0 ⇒ a > t ≥ 0 ⇒ 0 ≤ t < a

So, the particle moves to the right when 0 ≤ t < a