The vector position of a particle varies in time according to the expression r with arrow = 6.20 î − 5.40t2 ĵ where r with arrow is in meters and t is in seconds.

Question

(a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.)

(b) Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.)

(c) Calculate the particle's position and velocity at t = 4.00 s.

Answer 1

(a)

v = dr/dt

Evaluate the derivative, treating the unit vectors as constants.

(b)

a = d²r/dt²

Evaluate the derivative, treating the unit vectors as constants.

(c)

Evaluate r and v at t=4.00 s.