How Do You Calculate Distance and Velocity in Accelerated Motion?

[sunbunny]

Hey, this question has been drivning me crazy. I've tried making a velocity vs. time graph to help me sort out the different velocities, accelerations, displacements but no matter what i try or what type of equation i try, i just seem to be in a dead end. Here's the question:

A car accelerates from rest with a constant positive acceleration of
ax= +2.0m/s^2, then brakes with a constant negative acceleration of
ax= -4.0m/s^2, coming to a stop after a total time interval of 30s has elapsed. what are the distance traveled and the maximum veloicty reached by the car and what are the car's average velocity and average acceleration for this interval?

Thanks

 

[Locrian]

Well you have two separate kinematic problems here. The problem you are (probably?) having is that it does not tell you what the time is for each part, and you must find it.

The clue is that they are related. You know that the initial velocity of the first part (accelerating) is zero, and that the final velocity in the second part (decelerating) is zero. You also know the final velocity of the first part is equal to the initial velcoity of the second.

Recognizing this dramatically reduces the number of variables in your problem. Now write your equations out and see if you can make any progress. Let us know and we'll help more as you progress.

 

[BishopUser]

I know that $V_f = V_i + at$. With that equation we can do...

$$V_f = 0 + (2 \frac {m} {s^2})t_1$$ this describes the first part
$$0 = V_i + (-4 \frac {m} {s^2}t_2$$ this describes the second part

Right now there is 2 equations and 4 uknowns (vf, t1, vi, t2) so we need two more equations. Well we know that the final velocity of the first part must be the starting velocity of the next part so $$V_f = V_i$$. Looking to the problem we see that the total time is 30 seconds so we know that $$t_1 + t_2 = 30 seconds$$. From there you can do some subtitution and solve for one of the time intervals. Once you get that it should be easy.

 

[sunbunny]

Thank you both so much! i was never looking at it as final velocity of part 1 being equal to the inital velocity of part 2. Thanks so much!