Soru
A particle starting from rest revolves with uniformly increasing speed in a clockwise circle in the ry plane The center of the circle is at the origin of an zy coordinate system Att=0 the particle is at x=0.0,y=2.9mAtt=1.0s it has made one quarter of a revolution and is at x=y_(0),y=0.0 ) Part A Part B Part C Determine the average acceleration vector during this interval. Express your answer using two significant figures. Enter the z and y components of the acceleration separated by a comma. square
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4.5
(318 Oylar)
Leman
Kıdemli · 10 yıl öğretmeni
Uzman doğrulaması
Cevap
To determine the average acceleration vector, we need to find the change in velocity over the given time interval and divide it by the time taken.Given:Initial position: (x0, y0) = (0.0, 2.9) mFinal position: (x1, y1) = (2.9, 0.0) mTime interval: Δt = 1.0 sStep 1: Calculate the initial and final velocities.Since the particle starts from rest, the initial velocity is zero.The final velocity can be calculated using the formula for circular motion: v = Δθ / Δt, where Δθ is the change in angle and Δt is the time taken.In this case, the particle makes one-quarter of a revolution, which corresponds to a change in angle of 90 degrees or π/2 radians.Therefore, the final velocity is v = (π/2) / 1.0 = π/2 rad/s.Step 2: Calculate the change in velocity.The change in velocity is given by Δv = v - u, where u is the initial velocity and v is the final velocity.In this case, the initial velocity is zero, so the change in velocity is Δv = π/2 - 0 = π/2 m/s.Step 3: Calculate the average acceleration.The average acceleration is given by a = Δv / Δt, where Δv is the change in velocity and Δt is the time taken.In this case, the time interval is 1.0 s, so the average acceleration is a = (π/2) / 1.0 = π/2 m/s².Step 4: Express the answer using two significant figures.The average acceleration vector in the z and y components is:z-component: 0 m/s²y-component: 1.6 m/s²Therefore, the average acceleration vector during this interval is 0, 1.6 m/s².