Question

An automobile accelerates from rest at
2.5 m/s
2
for 29 s. The speed is then held
constant for 28 s, after which there is an acceleration of −3.8 m/s
2
until the automobile
stops.
What total distance was traveled?
Answer in units of km

Answer 1

hero can you help him

Answer 2

agent 47?

Answer 3

V_i=0
a=2.5(m/s^2)
t=29s
V_f - ?
this is the first part of the solution.

Answer 4

okay

Answer 5

V_f = V_i+a*t=0+2.5*29=72.5(m/s)

Answer 6

\[x=x_o+v_ot+\frac{1}{2}at^2\]

Answer 7

Final velocity is 72.5(m/s) <- this is before he decelerates.
@CliffSedge that formula wouldn't really work here.

Answer 8

So before he decelerates, the distance he has traveled is:
well actually @CliffSedge it would, lol sorry :)

Answer 9

lol

Answer 10

d = V_i * t + (1/2)a*t^2 = 0 + (1/2)*2.5*29^2 = 1051.25m
so before he starts decelerating he has traveled 1051.25 meters

Answer 11

@Agent47 , yes it does. i just used it.

Answer 12

Now once he starts decelerating:
V_i = 72.5 (m/s) <- he was travelling with this velocity before he started slowing down
V_f = 0 (m/s) <- the car comes to a stop
t = 28s
a = -3.8(m/s)
Again, use the same formula...

Answer 13

It's just for the first part, though.

Answer 14

d = V_i * t + (1/2)a*t^2 = 72.5*28 + (1/2)*(-3.8)*29^2 = 432.1m

Answer 15

So in total, he has traveled:
1051.25+432.1 = 1483.35m
now convert that..

Answer 16

The second part uses it (or a reduced form of it because of constant velocity) and v=a*t.
The third part uses that information and
\[\Delta v^2=2a \Delta x\]

Answer 17

to do so, just divide it by 1000, there are 1000 meters in a kilometer, so the final answer is:
1483.35/1000= 1.48335km

Answer 18

or about 1.5km

Answer 19

woah waitttt

Answer 20

The speed is then held constant for 28 s... my second part of the soln is wrong.

Answer 21

d = V_i * t + (1/2)a*t^2 = 0 + (1/2)*2.5*29^2 = 1051.25m
so before he starts decelerating he has traveled 1051.25 meters, and his speed is:
V_f = V_i+a*t=0+2.5*29=72.5(m/s)
Then he sticks with that speed for 28s, so he travels another: 28*72.5=28*72.5=2030m

Answer 22

And then it decelerates at -3.8m/s^2 until it comes to a stop, so, again:
V_i=72.5
V_f=0
a=-3.8
t - ? (I want to know what time it took him to stop)
a = (V_f-V_i)/t
-3.8=(0-72.5)/t
t=72.5/3.8=19.0789474s

Answer 23

and again this formula:
d = V_i * t + (1/2)a*t^2 saves the day, so during the deceleration, he has traveled:
d = V_i * t + (1/2)a*t^2 = 72.5*19.1+(1/2)*(-3.8)*(19.1)^2= 691.6m

Answer 24

Ok, now add them all up:
1051.25+2030+691.6 = 3772.85m, or 3.8km

Answer 25

okay

Answer 26

So basically you split questions like this one into three parts:
1) accelerating
2) constant
3) decelerating

Answer 27

can you help me with another problem