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A particle is at rest and at x=0 and y=0 at time = 0. The particle then moves in the x-y plane with an acceleration in m/s^2 of a = 5t^2 i + 5t j , where t is in seconds. Determine the magnitude of the particle's velocity vector in m/s at instant the y-component of the position vector ry = 8 meters.

Question

A particle is at rest and at x=0 and y=0 at time = 0. The particle then moves in the x-y plane with an acceleration in m/s^2 of a = 5t^2 i + 5t j , where t is in seconds. Determine the magnitude of the particle's velocity vector in m/s at instant the y-component of the position vector ry = 8 meters.

check_circleAnswer
Step 1
Given Jntormation -
At fime (tzo) x-0 cand yo
At time tzo) Vx =o and Uyzo
Acceleration vectpr a z 5ti+5tj
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Given Jntormation - At fime (tzo) x-0 cand yo At time tzo) Vx =o and Uyzo Acceleration vectpr a z 5ti+5tj

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Step 2
Given a5t and ay 5t
Velodty of the panticle
a dv
dt
dv adt
V
-Ja,dt
VxSstdt
Jstdt
Vyay dt
5
Vy
At time Cto) Vyzo
At time to), Vxo
C20
. V St
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Given a5t and ay 5t Velodty of the panticle a dv dt dv adt V -Ja,dt VxSstdt Jstdt Vyay dt 5 Vy At time Cto) Vyzo At time to), Vxo C20 . V St

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Step 3
Displacement is calculated
as
ds
dt
ds Vd t
S vdt
SVndt
Sx=
S-
37
Sy
6
At fime (to) Sy 0
(2
At time (t-o) S0
5t
S
C20
(2
help_outline

Image Transcriptionclose

Displacement is calculated as ds dt ds Vd t S vdt SVndt Sx= S- 37 Sy 6 At fime (to) Sy 0 (2 At time (t-o) S0 5t S C20 (2

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Physics

Kinematics

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