Aparticle initially located at the origin has an acceleration of = 2.00ĵ m/s2 and an initial velocity of i = 8.00î m/s. find (a) the vector position of the particle at any time t (where t is measured in seconds), (b) the velocity of the particle at any time t, (c) the position of the particle at t = 7.00 s, and (d) the speed of the particle at t = 7.00

(a) The vector position of the particle at any time t; is s(t) = (8i)t + (j)t²

(b) the velocity of the particle at any time is v = 8i + (2j)t

(c) the position of the particle at t = 7.00 s is 56i + 49 j at a distance of 74.4 m

(d) the speed of the particle at t = 7.00 is 16.12 m/s

The given parameters;

acceleration of the particle, a = 2 j m/s²

initial velocity of the particle, v = 8 i m/s

(a) The vector position of the particle at any time t;

(b) the velocity of the particle at any time

(c) the position of the particle at t = 7.00 s

(d) the speed of the particle at t = 7.00

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a. The particle has position vector

b. Its velocity vector is equal to the derivative of its position vector:

c. At , the particle has position

That is, it's 56.0 m to the right and 49.0 m up relative to the origin, a total distance of away from the origin in a direction of relative to the positive axis.

d. The speed of the particle at is the magnitude of the velocity at this time:

Then its speed at this time is

d is the correct answer