a car stands beside a series of poles 4 m apart. it accelerates from rest at a rate of 2m/s^2 for 4 seconds, maintains its constant velocity for another 4 seconds, and brakes to rest in 2 seconds. how many poles have the car passed?
can you please show me the solution? thanks
During acceleration,
x = xo + vo t + 1/2 at^2
x = 0m + (0m/s)(4s) + 1/2 (2 m/s^2)(4s)^2
x = 16 m
During constant velocity,
a = (vf - vo)/t
2 = (v - 0)/4
v = 8 m/s
x = vo t
x = 8 * 4
x = 32 m
During deceleration,
a = (vf - vo)/t
a = (0 - 8)/2
a = -4 m/s^2
x = xo + vo t + 1/2 at^2
x = 0m + (8 m/s)(2s) + 1/2(-4 m/s^2)(2s)^2
x = 16 - 8
x = 8
Total distance:
16 + 32 + 8 = 56
56 / 4 = 14 poles
vf=vo+a*t
vf=0+2*4
vf=8 m/s
d=4*8 > constant velocity distance=32
d_acceleration=v0*t+1/2*a*t^2=1*4^2=16
total d=48
48/4=12 poles
d=2*4=8= 2 more poles
=14 poles