A particle's trajectory is described by x =(12t3−2t2)m and y=(12t2−2t)m, where t is in s. a.)...

Question

Question

A particle's trajectory is described by x =(12t3−2t2)m and y=(12t2−2t)m, where t is in s.

a.) What is the particle's speed at t=4.0s ?

b.)What is the particle's direction of motion, measured as an angle from the x-axis, at t=4.0s ?

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Answer 1

Answer #1

a] Given that,

the x-coordinate of the particle in the x-y plane, x = 12t^3 - 2t^2

the y-coordinate of the particle in the x-y plane, y = 12t^2 - 2t

Differentiating both,

vx = dx/dt = 36t^2 - 4t

vy = dy/dt = 24t - 2

Putting the value of t = 4 s

vx = 36*4^2 - 4*4 = 560 m/s

vy = 24*4 - 2 = 94 m/s

v = sqrt[vx^2 + vy^2]

= sqrt[560^2 + 94^2]

= 567.83 m/s

b] arctan[94/560] = 9.53 degree

Answer 2

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