6. A particle is moving along a straight line. After t seconds the distance the particle has travelled is x cm, its velocity is v cms-1 and the acceleration a of the particle is given by the differential equation a = 0.035 v² Given that when t= 0, then x = 0 and v= 22 cms-1, calculate the velocity of the particle when t=2 seconds.

If u = (-1, 1, 1) and i = (0,0, 0), find the length and direction of u x i and i x ủ. Length of u x i is Direction of ủ x ở is (If ů x ủ does not have a direction, enter "none".) Length of i xu is ... Direction of v xũ is (If v xu does not have a direction, enter "none".)

If ů = (7,–6, 0) and i = (1, 1,0), find the length and direction of ủ x i and i x ū. Length of u x i is ... ... Direction of u xở is (If u X v does not have a direction, enter "none".) Length of i x ủ is Direction of ú xũ is (If i xủ does not have a direction, enter "none".)

In certain physical models, the nonhomogeneous term, or forcing term, g(t) in the equation ay" + by' + cy = g(t) may not be continuous, but have a jump discontinuity. If this occurs, a reasonable solution can still be obtained using the following procedure. Consider the following initial value problem. 240 if 0sts7T/6 y" + 4y' + 40y = g(t); y(0) = 0, y'(0) = 0, where g(t) = . if t> 7x/6 Complete parts (a) through (c) below. (a) Find a solution to the initial value problem for 0 sts 71/6. The solution for 0sts 7n/6 is y(t) = - 6 e -21 *cos 6t - 2 e - 2t sin 6t + 6 (Type an equation.) (b) Find a general solution for t> 71/6. The general solution for t> 7x/6 is y(t) = C, e-2 cos 6t + C, e -2t sin 6t (Type an equation. Do not use d. D. e, E, i, or I as arbitrary constants since these letters already have defined meanings.) (c) Now choose the constants in the general solution from part (b) so that the solution from part (a) and the solution from part (b) agree, together with their first…

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The instantaneous speed of a particle moving along one straight line isv(t) = ate−5t, where the speed v is measured in meters per second, the time t is measured in seconds, and the magnitude of the constant a is measured in meters per second squared. What is its maximum speed, expressed as a multiple of a? (Do not include units in your answer.)

We track the particle’s trajectory between t = 0 to t = T. During this interval, how much time transpires in the particle’s non-inertial reference frame?

An ant crawls on the surface of a ball of radius b in such a manner that the ant's motion is given in spherical coordinates by the equations r = b; phi = omega*t; theta = pi/2 * [1 + 1/4 * cos(400t)] Find the speed of the ant as a function of the time t. What sort of path is represented? by the above equations ?

An airline passenger drops a coin while the plane is moving horizontally at 260 m/s. Randomized Variables v = 260 m/sh = 1.6 m   How far does the coin travel horizontally in meters with respect to the Earth if it falls 1.6 m?

The position of an electron is given by 7 = 8.49tî – 5.75r2j + 1.68k, with t in seconds and 7 in meters. Att = 3.12 s, what are (a) the x-component, (b) the y-component, (c) the magnitude, and (d) the angle relative to the positive direction of the x axis, of the electron's velocity ů (give the angle in the range (-180°, 180°])? (a) Number Units (b) Number i Units (c) Number i Units (d) Number i Units > >