Question

The position of a particle is given by
r = 3.0 t i + 2.0 t?j +5.0 k
where, t is in seconds and the coefficients have the proper
units for r to be in metres.
(i) Find xft) and a(t) of the particles.
(ii) Find the magnitude and direction of v(t) at t = 2.0 s.
INCERTI. please explain in detail urgent​

Answer 1

v(t) = (3.0 i - 4.0t j)

a = -4.0 j

The position of the particle is given by:

r = 3.0t i -2.0t2 j +4.0 k

Velocity v of the particle is given as:

v = dr / dt = d (3.0t i -2.0t2 j + 4.0 k) / dt

∴ v = 3.0 i -4.0t j

Acceleration a of the particle is given by:

v = (32 + (-8)2)1/2 = (73)1/2 = 8.54 m/s

Direction, θ = tan-1(vy/vx)

= tan-1(-8/3) = -tan-1(2.667)

= -69.450

The negative sign indicates that the direction of velocity is below the x-axis