Physics Practice Problems Intro to 2D Motion Practice Problems Solution: The velocity vector v(t) measured in m/s for a par...

# 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.

###### Problem

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.

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