Solution: The velocity vector v(t) measured in m/s for a particle at time t is given as v(t) = [(3t + 4t3)î − 2ĵ] m/s, where t is in seconds.
[a] Find the units of the coefficients 3, 4, and 2 in the vector v.
[b] Find the average acceleration in the interval t = 0 to t = 2 seconds.
[c] Find the acceleration at t = 2 s.
[d] Say that at t = 0 the particle is at the origin, r(0) = 0. Find the position vector r(t).
[e] Eliminate t to give the equation of the trajectory x as a function of y.

The velocity vector * v*(t) measured in m/s for a particle at time t is given as

[a] Find the units of the coefficients 3, 4, and 2 in the vector * v*.

[b] Find the average acceleration in the interval t = 0 to t = 2 seconds.

[c] Find the acceleration at t = 2 s.

[d] Say that at t = 0 the particle is at the origin, * r*(0) = 0. Find the position vector

[e] Eliminate t to give the equation of the trajectory x as a function of y.