Starting at time from the origin with speed

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Starting at time

t = 0

from the origin with speed

1 \text{ 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 (1)

a_x = 1 \text{ ms}^{-2}

implies that when the particle is at the origin,

a_y = 1 \text{ ms}^{-2}

(2)

a_x = 0

implies

a_y = 1 \text{ ms}^{-2}

at all times (3) at

t = 0

, the particle's velocity points in the

x

-direction (4)

a_x = 0

implies that at

t = 1

s, the angle between the particle's velocity and the

x

axis is

45^\circ