# With acceleration work! simple!

1. Jan 24, 2004

plz help with acceleration work! simple!

hello im new here and will probably be here a lot if this goes well. im taking a college physics class and cannot figure out a few problems: 1. Coasting due south on your bicycle at 8.0 m/s, you encounter a sandy patch of road 6.4 m across. When you leave the sandy patch your speed has been reduced to 6.7 m/s. Assuming the bicycle slows with constant acceleration, what was its acceleration in the sandy patch? Give both magnitude and direction.
2. A 747 airliner reaches its takeoff speed of 168 mi/h in 34.9 s. What is the magnitude of its average acceleration?
3. Running with an initial velocity of +13 m/s, a horse has an average acceleration of -1.81 m/s2. How long does it take for the horse to decrease its velocity to +5.0 m/s?
4. As a train accelerates away from a station, it reaches a speed of 5.2 m/s in 5.0 s. If the train's acceleration remains constant, what is its speed after an additional 7.0 s has elapsed?

2. Jan 24, 2004

### jamesrc

Hi. Many people on these forums are happy to help you understand your work, but to really do a good job of that, we need to see what you've done (to gauge what concepts you understand). Try to keep that in mind in the future.

As for this problem set:

1. We know that the speed slowed from 8 m/s to 6.7 m/s over a distance of 6.4 meters under constant acceleration. The direction part is easy: since we see that the bike slowed down, we know that the acceleration was in the opposite direction of its velocity, i.e., it accelerated due north. You should have a number of kinematic equations at your disposal at this point. I recommend using the following equation to find the acceleration in this problem:

$$v^2 - v_o^2 = 2a\Delta x$$

where a is the acceleration, v is the final velocity of the biker, vo is the initial velocity of the biker, and &Delta;x is the distance over which the bike accelerates (6.4 m). You will find a<0, confirming the earlier statement about the direction of the acceleration.

2. For this problem, you have the time the plane takes to go from rest to some velocity and are asked for the magnitude of the average acceleration. The equation I thnk you'll want to use here is:

$$v = v_o + a\Delta t$$

again solving for a

$$a = \frac{\Delta v}{\Delta t}$$

which is a true statement for constant accelerations (or finding average accelerations). It simply says that the acceleration is the change in velocity per the corresponding change in time.

3. Use the same equation as in #2, except, this time a is known and &Delta;t is unknown.

4. This one's a two-parter: find the acceleration from the first part of the trip, then use that to solve for the final velocity. Remember that the final velocity for the first part of the trip becomes the initial velocity for the second part of the trip.