How Do You Calculate Acceleration in Different Scenarios?

[adversary]

please help with acceleration work! simple!

hello I am new here and will probably be here a lot if this goes well. I am 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?
thanks for all your help!

 

[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, v_o 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.

 

[M98Ranger]

Sure, I would be happy to help with acceleration work! Acceleration is an important concept in physics and can be a bit confusing at first, but once you understand the basics, it becomes much simpler.

Let's start with a definition of acceleration. Acceleration is the rate of change of velocity over time. In other words, it is how quickly an object's speed or direction changes.

Now, let's take a look at the first problem. You are coasting on your bicycle at a constant speed of 8.0 m/s, and then you encounter a sandy patch of road. After leaving the sandy patch, your speed has decreased to 6.7 m/s. This change in speed tells us that there was an acceleration happening. We can use the formula for acceleration, a = (vf - vi)/t, to solve for the acceleration in this case.

First, we need to determine the initial velocity (vi) and the final velocity (vf). Since you started at a constant speed of 8.0 m/s and ended at 6.7 m/s, we can plug those values into the formula. a = (6.7 m/s - 8.0 m/s)/t. The time (t) is not given in this problem, so we cannot solve for the acceleration just yet. However, we can use the fact that the bicycle slows with constant acceleration to determine the direction of the acceleration.

Since the bicycle is slowing down, the acceleration must be in the opposite direction of the motion, which is south in this case. Therefore, the acceleration is -x m/s^2, where x is the magnitude of the acceleration. Now, we can rewrite the formula as -x = (6.7 m/s - 8.0 m/s)/t.

To solve for x, we need to know the time (t). We can use the fact that the road is 6.4 m across to find the time. We know that the bicycle's speed is changing at a constant rate, so we can use the average speed to calculate the time. Average speed is equal to the total distance traveled divided by the total time taken. In this case, the total distance is 6.4 m, and the total time is the time it took to cross the sandy patch plus the time it took to slow down to 6.7 m/s. So, we can set up the equation: 6.4 m/