Question

Starting at time $t =0$ from the origin with speed $1\, ms ^{-1}$, a particle follows a two-dimensional trajectory in the $x-y$ plane so that its coordinates are related by the equation $y=\frac{x^{2}}{2}$. The $x$ and $y$ components of its acceleration are denoted by $a _{ x }$ and $a _{y}$, respectively Then

• A. $a _{ x }=1 \,ms ^{-2}$ implies that when the particle is at the origin, $a _{ y }=1 \,ms ^{-2}$
• B. $a _{ x }=0$ implies $a _{ y }=1\, ms ^{-2}$ at all times
• C. at $t =0$, the particle's velocity points in the $x$-direction
• D. $a _{ x }=0$ implies that at $t =1 s$, the angle between the particle's velocity and the $x$ axis is $45^{\circ}$

Answer 1

Answer: (A), (B), (C), (D)

$a _{ x }=1 \,ms ^{-2}$ implies that when the particle is at the origin, $a _{ y }=1 \,ms ^{-2}$

Answer 2

(A) $a _{ x }=1 \,ms ^{-2}$ implies that when the particle is at the origin, $a _{ y }=1 \,ms ^{-2}$
(B) $a _{ x }=0$ implies $a _{ y }=1\, ms ^{-2}$ at all times
(C) at $t =0$, the particle's velocity points in the $x$-direction
(D) $a _{ x }=0$ implies that at $t =1 s$, the angle between the particle's velocity and the $x$ axis is $45^{\circ}$