Question

An automobile accelerates from rest at 2.0 m/s2 for 20 s. The speed is then held constant for 20 s, after which there is an ac- celeration of -3.0 m/s? until the automobile stops. What is the total distance traveled?

Answer 1

Answer:

$1446.7m$

Explanation:

You need to look at this in 3 separate stages, and then sum thedistance from each stage:

Stage 1)

a=2

t=20

$V_0$=0

$s=V_0t+\frac{1}{2}g t^2$

$x=400m$

We also need to find the final velocity $v=a*t=20*2=40m/s$

Stage 2)

a=0

v=40

t=20

$x=vt$

$x=800m$

Stage 3)

a=-3

$v_0$=40

$v$=0

$v^=v_0^2 + 2 a x\\0=40^2+2*(-3)x\\x=266.7m$

So the total distance is $x=400+800+266.7=1466.7m$