How to do 19? A particle\'s position as a function of time is given by 18. What

Question

How to do 19?

A particle's position as a function of time is given by 18. What is the magnitude of the particle's velocity at t1.0s? (a) 1 (b) 2.0% (c) 2.8m (d) 3.9m 19. Which unit vector is closcst to the direction of the particle's velocity at t1.0s? (c) j (d) -j (e) k 20, what is the angle between the particle's u and a at t = 2.0s? (a) 0° (b) 30° (c) 45° (d) 60° 21. The angle between the velocity and acceleration vectors is such that at t 2.0s the particle is (a) Speeding up and turning (b) Slowing down and turning (c) **Going at a constant speed and turning (d) Speeding up and not turning

Explanation / Answer

given position of particle as a funciton of time
r(t) = 2msin(pi*t)i + 2mcos(pi*t) j

velocity = v = dr/dt
v(t) = 2m*pi*cos(pi*t)i - 2m*pi*sin(pi*t)j

19. at t = 1s
v(1) = 2m*pi[cos(pi)i - sin(pi)j]
v(1) = 2m*pi[-i]

hence the unit vector at t= 1 s along the velocity is -i
hence answer is option b)

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