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- The coordinates of a bee flying in the xy-plane are given by x(t) = At and y(t) = C - Bt², where A = 3.2 m/s, B = 1.4 m/s², and C= 2.5 m. Calculate the velocity and acceleration vectors of the bee as a function of time. Write your answers in unit vector notation.arrow_forwardA computer model displays the motion of a particle on a coordinate system in real time. At time t = 0, the particle is at the origin of the coordinate system and has velocity components vx = 0 and vy = 6.0 m/s. The particle has acceleration components of ax = −4.8 m/s2 and ay = 0. (Part A) What are the x and y positions of the particle, in meters, at t = 4.0 s? x = ? y = ? (Part B) What are velocity components of the particle, in m/s, at t = 4.0 s? Vx = ? Vy = ?arrow_forwardA computer model displays the motion of a particle on a coordinate system in real time. At time t = 0, the particle is at the origin of the coordinate system and has velocity components vx = 0 and vy = 6.8 m/s. The particle has acceleration components of ax = -5.2 m/s² and ay = 0. (a) What are the x and y positions of the particle, in meters, at t = 4.5 s? X = y = Vx m (b) What are velocity components of the particle, in m/s, at t = 4.5 s? m/s m/s = m (c) How does the speed of the particle change from t = 0 to t = 4.5 s? O The particle's speed increases with time. O The particle's speed decreases with time. O The particle's speed remains constant. O The particle's speed increases and then decreases with time.arrow_forward
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- A computer model displays the motion of a particle on a coordinate system in real time. At time t = 0, the particle is at the origin of the coordinate system and has velocity components vx = 0 and vy = 7.2 m/s. The particle has acceleration components of ax = −3.2 m/s2 and ay = 0. (a) What are the x and y positions of the particle, in meters, at t = 4.5 s? x = ? m y = ? m (b) What are velocity components of the particle, in m/s, at t = 4.5 s? vx = ? m/s vy = ? m/s (c) How does the speed of the particle change from t = 0 to t = 4.5 s? a) The particle's speed remains constant. b) The particle's speed increases and then decreases with time. c) The particle's speed decreases with time. d) The particle's speed increases with time.arrow_forwardThe position of a particle in the xy-plane at time t is r(t) = (e¹) 1 + (40 e²¹) ₁. particle. Then find the particle's velocity and acceleration vectors at t = In 7. The equation for the path of the particle is y= j. Find an equation in x and y whose graph is the path of thearrow_forwardIf the vector components of the position of a particle moving in the xy plane as a function of time are x = (2.8 m/s2)t2 and y = (6.4 m/s3)t3, at what time t is the angle between the particle's velocity and the x axis equal to 45°?arrow_forward
- The velocity of a particle is given by v ={16t^2i +4t^3j + (5t +2)k} m/s, where t is in seconds. If the particle is at the origin when t = 0, determine the magnitude of the particle’s acceleration when t = 2 s. Also, what is the x, y, z coordinate position of the particle at this instant?arrow_forwardA jet plane is flying at a constant altitude. At time t1 = 0, it has components of velocity vx = 90 m/s, vy = 110 m/s. At time t2 = 30.0 s, the components are vx = -170 m/s, vy = 40 m/s. (a) Sketch the velocity vectors at t1 and t2. How do these two vectors differ? For this time interval calculate (b) the components of the average acceleration, and (c) the magnitude and direction of the average acceleration.arrow_forwardThe equation r(t) = ( sin t)i + ( cos t)j + (t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. π Then write the particle's velocity at t= as a product of its speed and direction. The velocity vector is v(t) = (i+j+ k.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning