General Physics Q: Find Acceleration, Velocity, Speed

In summary, acceleration is the rate of change of velocity over time, velocity is the rate of change of position over time (including direction), and speed is the rate of change of distance over time (excluding direction). Acceleration can be calculated by dividing the change in velocity by the change in time or by taking the second derivative of the position function with respect to time. It determines how quickly an object's velocity changes, causing it to speed up or slow down. Average acceleration is the change in velocity over a certain interval, while instantaneous acceleration is the acceleration at a specific moment in time. These parameters can be used to describe an object's motion by understanding their relationships.
  • #1
ken62310
13
0
a general physics q please help!

A bob rotates clockwise in a vertical circle at the end of a 1 m long rope. In the pint, where the rope makes the horizontal to the right, the acceleration of the bob is (-2i+3j)m/s^2. At that instant
-sketch the acceleration vector and find its magnitude,
-find tangential and radial acceleration,
-find velocity and speed of the ball
-is the speed increasing or decreasing in this point?
 
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  • #2
Show us what you have done. Explain what you are confused about.
 
  • #3


To find the acceleration, velocity, and speed of the bob, we can use the kinematic equations of circular motion. First, we can sketch the acceleration vector at the point where the rope makes the horizontal to the right. This vector will have a magnitude of √(4+9) = √13 m/s^2 and a direction of 45 degrees below the horizontal.

Next, we can find the tangential and radial acceleration using the formula a_t = v^2/r and a_r = v^2/r, where v is the velocity and r is the radius of the circle. Since the radius is 1 m, the tangential acceleration will be equal to v^2, and the radial acceleration will be equal to v^2/1 = v^2. Solving for v, we get v = √(a_t*r) = √(4*1) = 2 m/s. This is the velocity of the bob at the point where the rope makes the horizontal to the right.

To find the speed, we can use the formula v = ω*r, where ω is the angular velocity. Since the bob is rotating at a constant speed, we can assume that ω is constant. Therefore, the speed of the bob will be equal to the velocity, which is 2 m/s.

Since the acceleration vector is pointing in the opposite direction of the velocity vector, we can conclude that the speed is decreasing at this point. This means that the bob is slowing down as it moves along the circle.
 

1. What is the difference between acceleration, velocity, and speed?

Acceleration is the rate of change of velocity over time. Velocity is the rate of change of position over time, and includes both speed and direction. Speed is the rate of change of distance over time, and does not include direction.

2. How do you calculate acceleration?

Acceleration can be calculated by dividing the change in velocity by the change in time. It can also be found by taking the second derivative of the position function with respect to time.

3. How does acceleration affect an object's motion?

Acceleration determines how quickly an object's velocity changes. A positive acceleration will cause an object to speed up, while a negative acceleration (also known as deceleration) will cause an object to slow down. If an object has a constant acceleration, its velocity will change by the same amount every second.

4. What is the difference between average and instantaneous acceleration?

Average acceleration is the change in velocity divided by the change in time over a certain interval. Instantaneous acceleration is the acceleration at a specific moment in time, and can be found by taking the derivative of the velocity function with respect to time.

5. How can you use acceleration, velocity, and speed to describe an object's motion?

Acceleration, velocity, and speed are all important parameters that can be used to describe an object's motion. Acceleration tells us how quickly an object's velocity is changing, velocity tells us the speed and direction of the object, and speed tells us how fast the object is moving. By looking at the relationships between these parameters, we can get a better understanding of an object's motion.

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