# Distance Traveled By A Car-Kinematics Problem

1. Oct 29, 2009

### haengbon

1. The problem statement, all variables and given/known data

a car traveling due east on a straight road and accelerates at a constant rate for 10(s) increasing its velocity from rest to 40 m/s. It then travels at a constant velocity for 5s and accelerates at a steady rate for the next 5s to a velocity of 20m/s. It travels at this velocity for 10s and then accelerates rapidly to a stop at a time of 2s. What is the total distance traveled by the car?

All I know is, the answer NEEDS TO BE 770m. I'm trying to find the soltuion :(

2. Relevant equations

none /:)?

3. The attempt at a solution

I tried solving it first by drawing a diagram and then , paired up (40 m/s, 10s), (40m/s,5s) , (20m/s,5s), (20m/s,10s), (v=?,2s)

then, I solved for the acceleration for each with V=Vo + at. after which, I solved for each of their distances with V(^2) = Vo(^2) + 2ad.

for example,

G: 40 m/s , 10s

V = Vo+ at
40 = 0 + a(10)
a = 4 m/s^2

1600 = 0 + 2(4)d
d = 200 m

I did the same thing with all the others and after reaching (20 m/s,10s), I got 900. I stopped there and didn't solve further cause I thought I wouldn't get the right answer anymore even if I did solve for (v=?,2s) .

Can someone please guide me? :( I need to find out how to solve this because it would most likely be in the exam I need to pass just days away :( It looked simple at first but I'm going crazy solving it

2. Oct 29, 2009

### ApexOfDE

3. Oct 29, 2009

### rl.bhat

Draw the time-velocity graph.
To find the total distance traveled by the car, find the area bounded by the graph with x-axis. It contains 2 triangles, two rectangles and one trapezium.

4. Oct 29, 2009

### haengbon

how do I draw a time-velocity graph :((? I'm sorry but I really don't know how to -___-

5. Oct 29, 2009

### haengbon

I did and I'm sure It's wrong :D I think my formulas is wrong

6. Oct 29, 2009

### VelvetRebel

Are 2 of your accelerations negative? If not, then I believe this is where you are making the mistake. For example, if you are going from 40 m/s to 20 m/s in 5s, this will have a negative acceleration since you are decreasing in velocity.

7. Oct 29, 2009

### rl.bhat

Take time on x-axis and velocity in y-axis.
Answer to the first part is correct.
For second part, d2 = v*t.
For third part vi = 40 m/s and vf = 20 m/s. Do the calculation as in the first part.
repeat the same thing for reaming parts.

Last edited: Oct 30, 2009
8. Oct 30, 2009

### haengbon

when velocity changes and decreases does that mean it has a negative acceleration? because it's slowing down right?

I tried this and it worked :) thank you thank you!