A particle\'s trajectory is described by x =(12 t 32 t 2)m and y =(12 t 22 t )m,

Question

A particle's trajectory is described by x =(12t32t2)m and y =(12t22t)m, where t is in s.

Part A

What is the particle's speed at t=0s ?

2

Correct

Part B

What is the particle's speed at t=3.0s ?

Express your answer using two significant figures.

??

Part C

What is the particle's direction of motion, measured as an angle from the x-axis, at t=0  s ?

Express your answer using two significant figures.

Part D

What is the particle's direction of motion, measured as an angle from the x-axis, at t=3.0s ?

Express your answer using two significant figures.

???

2

Explanation / Answer

A)

vx = dx/dt

= 36*t^2 - 4*t

vy = dy/dt

= 24*t - 2

at t = 0s,

vx = 36*0^2 - 4*0

= 0

vy = 24*0 - 2

= -2 m/s

speed, v = sqrt(vx^2 +vy^2)

= sqrt(0^2 + 2^2)

= 2 m/s

B)

at t = 3s,

vx = 36*3^2 - 4*3

= 312 m/s

vy = 24*3 - 2

= 70 m/s

speed, v = sqrt(vx^2 +vy^2)

= sqrt(312^2 + 70^2)

= 320 m/s

C) 270 degrees counter clockwise from +x axis

D) theta = tan^-1(vy/vx)

= tan^-1(70/312)

= 12.6 degrees

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