Question

A truck on a straight road starts from rest, accelerating at 2.00 m/s2 until it reaches a speed of 20.0 m/s. Then the truck travels for 20.0 s at constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional 5.00 s. (a) How long is the truck in motion? (b) What is the average velocity of the truck for the motion described?

a) I use the equation

V_xf = V_xi + a_x(t)

I know
V_xf = 20.0m/s
V_xi = 0m/s
ax = 2.0
thus I solve for t and get 10seconds
and then take 5 seconds to break after 20 seconds of driving

so for a) 10 + 20 + 5 = 35 seconds

Answer 1

for part b)
I need to use the formula

Delta x/Delta t = average velocity
Need to find xf, knowing xi = 0
Thus I use the formula

x_f = x_i + V_xi(t) + (1/2)a_x(t)^(2)
x_f = 0 + 0(10) + (1/2)(2.0)(10)^(2)
x_f = 100m

so for the first 10 seconds the truck traveled 100ms

At a speed of 20m/s

20m/s = xm/20s
20*20 = x
x = 400

thus we have 100+400 = 500m

then it slows down from 500m to x_f

thus I use the equation

x_f = x_i + (1/2)(V_xf + V_xi)t
x_f = 500 + (1/2)(0 + 20)(5)
x_f = 500 + 50
x_f = 550

therefore the total distance traveled is 550m

Is this correct?

Answer 2

crud I forgot to calculate average velocity

550/35 = 16m/s

thus

V_xavg = 16m/s

Answer 3

Yep it seems ok.
Total dist traveled = first part + second part + third part= 100+400+50=550 m
Total time=10+20+5=35 sec.