Problem 4.8 A particle\'s trajectory is described by x = ( -2t2) m and y = (r-2t

Question

Problem 4.8 A particle's trajectory is described by x = ( -2t2) m and y = (r-2t) m where t is in s. t Part A What is the particle's speed at t = 0 s ? ANSWER: Part B What is the particle's speed at t = 5.0s ? Express your answer using two significant figures. ANSWER: 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. ANSWER: counterclockwise from the +x axis. Part D What is the particle's direction of motion, measured as an angle from the x-axis, at t-5.0s? Express your answer using two significant figures. ANSWER: counterclockwise from the +x axis.

Explanation / Answer

x=((1/2)t^3 - 2t^2)

y=((1/2)t^2-2t)

dx/dt= 3/2*t^2 - 4t

dy/dt = t - 2

Putting the values of t in these gives the x and y components of velocity of the particle

t = 0 x-comp. of v= 0 m/s and y-comp. of v= -2 m/s

speed = [(0)²+(*2)²] = 2m/s ---------------------part 1)

t =5   x-comp. of v= 17.5 m/s and y-comp. of v= 3 m/s

speed= [(17.5)²+(*3)²] = 17.75m/s ---------------part 2)

particle's direction = arctan Vy/Vx
at t = 0 arctan Vy/Vx = arctan (0/-2) = 0° ANS------part 3)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.