A particle’s acceleration is (4.0 i+3.0 j) m/s2. At t=0, its position and velocity are zero. (a) What are the particle’s position and velocity as functions of time? (b) Find the equation of the path of the particle. Draw the x- and y-axes and sketch the trajectory of the particl
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A particle’s acceleration is (4.0 i+3.0 j) m/s2. At t=0, its position and velocity are zero. (a) What are the particle’s position and velocity as functions of time? (b) Find the equation of the path of the particle. Draw the x- and y-axes and sketch the trajectory of the particle.
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- A particle’s acceleration is (4.0iˆ+3.0jˆ)m/s2.(4.0i^+3.0j^)m/s2. At t = 0, its position and velocity are zero. (a) What are the particle’s position and velocity as functions of time? (b) Find the equation of the path of the particle. Draw the x- and y-axes and sketch the trajectory of the particle.A particle initially is moving at a velocity with Cartesian components (5.0 m/s, 4.0 m/s) and 5.6 s later it is moving at a velocity with components (8.0 m/s, 0.0 m/s). What is the magnitude of its average acceleration, in m/s2?A 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.
- An ant crawls on the floor along the curved path shown in Figure P3.4. The ant's positions and velocities are indicated for times tI=0 and tf=5.00 s. Determine the x- and y- components of the ant's (a) displacement, (b) average velocity, and (c) average acceleration between the two times. Chapter 3, Problem 4P , An ant crawls on the floor along the curved path shown in Figure P3.4. The ant's positions and Figure P3.4A particle is moving in the i- j plane with an acceleration of (1 – t)i +tj where t is the time. The particle is projected from the with an initial velocity of 3/2ims . Find the displacement of the particle at time t and the value of t when it is moving in the direction of motion. What is the angle between its velocity and displacement at this time?A particle moves along the x-axis. The function x(t) gives the particle’s position at any time t ≥ 0: x(t) = t3-4t2+3t-2 a) What is the particle’s velocity v(t) at t=3s? b) What is the particle’s acceleration a(t) at t=3s? What is the direction of the particle’s motion at t=2s? at t=3s, is the particle’s speed increasing, decreasing, or neither?
- 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 = 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 = ?A particle moving along the xx-axis has its position described by the function x=(4t3+5t+2)mx=(4t3+5t+2)m, where t is in s. At t = 2 s, what is the particle's velocity At t = 2 s, what is the particle's acceleration?The bacterium Escherichia coli (or E. coli) is a single-celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, these bacteria swim along zig-zag paths at a constant speed of 20 μm/s. The figure shows the trajectory of an E. coli as it moves from point A to point E. Each segment of the motion can be identified by two letters, such as segment BC. (Figure 1) Figure y (μm) 40 30 20 10- 0 -10- -20 -30 A -40 C E D B 10 20 30 40 50 60 70 80 90 100 1 of 1 x (μm) For the segment AB in the bacterium's trajectory, calculate the x and y components of its displacement. Express your answers in micrometers to two significant figures separated by a comma. ΨΕ ΑΣΦ XAB, YAB Submit = Part B Previous Answers Request Answer X Incorrect; Try Again; One attempt remaining ? um For the segment BC in the bacterium's trajectory, calculate the x and y components of its displacement. Express your answers in micrometers to two significant…
- 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 = 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 = m = m (b) What are velocity components of the particle, in m/s, at t = 4.5 s? Vx m/s m/s (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.The velocity of a particle (in meters per second) is given by v = 16t²i + 4t³j+ (5t + 2)k, 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?The position vector of a particle is given as r = (t^2-6t+8)i + (t^2-9)j Find the magnitude and direction of the particle’s position, velocity, and acceleration at ? = 2?. Find the magnitude and direction of the particle’s displacement, average velocity and average acceleration for the time period ? = 2? to ? = 3?.