At t $=0$s$,$ a particle is at rest at x$0=128$m$.$ It has acceleration a $=4$m$/$s$2.$

a$)$ Determine the velocity of the particle at t $=2$s$.$

b$)$ Determine the position of the particle at t $=2$s$.$

c$)$ Determine the speed of the particle as it passes the point x $=56$m$.$

d$)$ Determine the speed of the particle as it passes the point x $=30$m$.$

$2.$ A Jeep and a motorcycle are at rest, side by side, at a stoplight. When the light turns green,

the motorcycle accelerates at $4$m$/$s$2$ for $5$s$,$ while the Jeep accelerates at $2$m$/$s$2$ for $10$s$.$ Once

each vehicle stops accelerating, it maintains a constant speed.

a$)$ Determine the speed of the motorcycle at

i$.$ t $=5$s

ii$.$ t $=10$s

b$)$ Determine the speed of the Jeep at

i$.$ t $=5$s

ii$.$ t $=10$s

c$)$ Determine the displacement of the motorcycle at

i$.$ t $=5$s

ii$.$ t $=10$s

d$)$ Determine the displacement of the Jeep at

i$.$ t $=5$s

ii$.$ t $=10$s

Fall $2024$ Problem Set #$5$