Question

An object travels with a constant acceleration for 10 s. The vectors in the figure represent the final and initial velocities. Move the endpoints of the lines in the plots to graph the x-component of the velocity versus time, the y-component of the velocity versus time, and the y-component of the acceleration versus time. 20 m/s 30° Velocity vs. time 20 16 12 30V 6 2 20 m/s 2 -6 -8 -10 -12 -14 about usca privacy policy terms of use contact us help

Answer 1

The initial velocity of the object is, 7; = (v, sin 8 ) î - (v;cos ) = (20 m/s)sin 30°î -((20 m/s) cos 30º) į = (10 m/s) î – (17.32 m/s) Î The final velocity of the object is, 7, =(v, cos 6)ỉ +(v, sin ) = (20 m/s)cos 30°î +((20 m/s) sin 30°) į = (17.32 m/s) { +(10 m/s) The graph between x-component of the velocity and time is as follows: time(seconds) X-component of velocity(m/s) 10 17.32 101 x component of velocity - 4 8 - 10 12 6 time (seconds)

The graph between y-component of the velocity and time is as follows: time(seconds) y-component of velocity(m/s) -17.32 10 10 y component of velocity 10 12 time (seconds) The acceleration of the object is,

ā=1 vs - v Δt (17.32 m/s) î +(10 m/s) Î-((10 m/s) i – (17.32 m/s);) 10 s-Os _ (7.32 m/s) î – (7.32 m/s) Î 10 S-os = (0.732 m/s) î -(0.732 m/s) į Therefore, the magnitude of the acceleration is, a= V(0.732 m/s) +(-0.732 m/s)? = 1.035 m/s2 The acceleration is constant for the first 10 s. Hence, the graph between acceleration of the object and time is as follows:

time(seconds) acceleration(m/s^2) 1.035 1.035 10 acceleration 2 4 8 10 12 6 time (seconds)