Motion along a straight line (Finding acceleration).

[Sarah Sposato]

Figure 2-24 shows a red car and a green car that move toward each other. Figure 2-25 is a graph of their motion, showing the positions xg0 = 270 m and xr0 = -35 m at time t = 0. The green car has a constant speed of -20 m/s and the red car begins from rest. What is the acceleration magnitude of the red car?
The graph of their motion shows the two cars intersect their position at t = 12 seconds.

I started out by interpreting the labels and information.
Xo (g) : 270m
Xo (r) : -35m
(Constant) V (g) : -20m/s
Vo (r) : 0 m/s.
t = 12 seconds.

1. I used the formula X = Xo + ( V - Vo/ 2 )t to get the position at which the cars meet.

X = 270 + (-20/2)12

X = 150m,

Then I used the formula X = Xo + Vot + 1/2at^2 to get the acceleration of the red car.

150 = -35 + 0 (12) + 1/2a(12)^2.

This yielded a = 1.68 m/s*sThe answer is supposed to be a= 0.9m/s*s.Where did I go wrong? Was my interpretation of the data incorrect? Or just the way I plugged in the data?

 

[SteamKing]

Can you post the two figures associated with this problem?

 

[Sarah Sposato]

 

[SteamKing]

Figure 2-24 shows a red car and a green car that move toward each other. Figure 2-25 is a graph of their motion, showing the positions xg0 = 270 m and xr0 = -35 m at time t = 0. The green car has a constant speed of -20 m/s and the red car begins from rest. What is the acceleration magnitude of the red car?
The graph of their motion shows the two cars intersect their position at t = 12 seconds.

I started out by interpreting the labels and information.
Xo (g) : 270m
Xo (r) : -35m
(Constant) V (g) : -20m/s
Vo (r) : 0 m/s.
t = 12 seconds.

1. I used the formula X = Xo + ( V - Vo/ 2 )t to get the position at which the cars meet.

Why? The green car has a constant speed of -20 m/s, according to the problem statement.

What's the correct formula for finding distance traveled for an object traveling at constant speed?

X = 270 + (-20/2)12

X = 150m,

This distance X doesn't appear to be correct, just by looking at the graph which shows the motion of the cars versus time.

Then I used the formula X = Xo + Vot + 1/2at^2 to get the acceleration of the red car.

150 = -35 + 0 (12) + 1/2a(12)^2.

This yielded a = 1.68 m/s*s

The answer is supposed to be a= 0.9m/s*s.

Where did I go wrong? Was my interpretation of the data incorrect? Or just the way I plugged in the data?

I think the second part of your work went wrong because you made the mistakes in the first part, as discussed above.