The velocity V of a particle moving in the xy plane is given by V = (5.5t - 4.2t2) i + 8.7 j, with V in meters per second and t (> 0) in seconds. At t = 1.9 s and in unit- vector notation, what are (a) the x component and (b) the y component of the acceleration? (c) When (if ever) is the acceleration zero? (d) At what positive time does the speed equal 10 m/s?

The record of acceleration measurements made on an experimental vehicle during its rectilinear motion is shown by the full line on the figure below. Use the dotted approximation and calculate the velocity at 2 and 4 seconds. Find the distance travelled from =0 tot =4 seconds. [Answer: 98.1m/s, 196.2 m/s, 360m] 10 g 5g t, sec Acceleration 4,

Please answer completely, step by step with brief explanation

A turtle crawls along a straight line, which we’llcall the x-axis with the positive direction to the right. The equationfor the turtle’s position as a function of time is x 1t2 = 50.0 cm +(2.00 cm/s)t - (0.0625 cm/s2)t2. Sketch graphs of x versus t, vx versus t, and ax versus t, for the time interval t = 0 to t = 40 s.

In the figure, link 2 rotates with constant angular velocity 02. A slider link 3 moves outwards with a constant relative velocity Vop, where Q is a point on slider 3 and P is a point on link 2. The magnitude and direction of Coriolis component of acceleration is given by Qon 3 V ОР P on 2 (A) 2002 Vop; direction of Vop rotated by 90° in the direction 002 (B) ₂ Vop; direction of Vop rotated by 90° in the direction 00₂ (C) 2002 Vo/p; direction of Vop rotated by 90° opposite to the direction of 2 (D) ₂ Vqp; direction of Vop rotated by 90° opposite to the direction 002

The known angular velocity of link AB is wAB and the unknown angular velocity of link BC is wBc. Determine the velocity vectors V B, V C, and w BC using a relative motion analysis. Reduce/simplify all expressions as far as possible. The only parameters that should appear in your symbolic solution include wAB, LAB, LBc, 0, and ø. Finally, numerically evaluate the three velocity vectors using values LAB = 2 m, LBC 1.5 m, WAB = 0.25 rad/s, 0 = 30°, and ø = 10°. В LBC LAB W BC WAB

Q No 1:  The position of a particle moving along the x-axis is given by x=A+B t3,              where A=9.75 cm and B=1.50cm/s3.consider the time interval t=2 to t=3s and             calculate (a).the average velocity; (b).the instantaneous velocity at t=2s;(c). the             instantaneous velocity at t=3s;(d). the instantaneous velocity at t=2.5s;(e). the             instantaneous velocity when the particle is midway between its positions at t=2s             and t=3s.

The plot below shows the acceleration of a mass placed at the end of a beam as it oscillates: 20 Which we model as: Acceleration (m/s²) 15 10 5 0 -5 -10 -15 -20 0.5 1 Wd 1 1.5 1 2 = wn√1 y(t) = Ae-3wnt sin(wat) y(t) = Ae-Ct sin 1 2.5 Time (s) = 2π T 2π T 1+ 3 2π We will use MATLAB to find the decay constant C and the period T. We can then use these to calculate the damping ratio and the natural frequency @n, using: 3.5 T 4 2 and C = {wn O data zeros peaks decay fit 4.5 Using the information above, derive the expression shown below for the damping ratio 3. 1 3 = 5

Please do this caredully.

Thermal conductivity k is a measure of the ability of a material to conduct heat. For conduction heat transfer in the x-direction through a surface normal to the x-direction, Fourier’s law of heat conduction is expressed as: Q=-kA.dT/dx   where ?̇ is the rate of heat transfer and A is the area normal to the direction of heat transfer. Determine the primary dimensions of thermal conductivity (k). Look up a value of k and verify that its SI units are consistent with your result. Write a set of primary SI units for k.