Acceleration/Velocity vectors question

  • Thread starter SlammedMax
  • Start date
  • Tags
    Vectors
In summary, an object undergoes acceleration of 2.3i+3.6j m/s^2 over a 10s interval. Its velocity at the beginning of the interval was 10i-21j m/s. The speed changed by 13 m/s and the direction changed by 88.9º. The process for finding the direction change involved setting up vector graphs and using the law of sines to find the angles at the origin. For finding the speed change, you simply take the magnitudes of the velocity vectors and subtract them.
  • #1
SlammedMax
3
0
ok, homework question
An object undergoes acceleration of 2.3i+3.6j m/s^2 over a 10s interval. At the end of this time, its velocity is 33i+15j m/s.
A. What was its velocity at the beginning of the 10s interval?
B. By how much did its speed change?
C. By how much did its direction change?

I know how to do part A, as I did it like this:
(2.3i+3.6j)10=23i+36j ; 33i+15j-23i-36j=10i-21j
I am stumped on parts 2 and 3, I need help on where to begin on those.
 
Physics news on Phys.org
  • #2
ok, now i just found part c. I just set up the vector graphs, and did the law of sines to find the angles at the origin. They came out to be 24.4 and 64.5, so added together to get the total direction change, I came out with 88.9º. In the back of the book, that is correct. Now, i should be able to get part b, so we'll see.
 
  • #3
ok, now i found part b. I finally realized that all I had to do was take the magnitudes of the velocity vectors and subtract them. Came out to 13 m/s, which is the correct answer. I guess I just needed to take the time and graph em, haha...dont need the help...yet.
 

FAQ: Acceleration/Velocity vectors question

1. What is the difference between acceleration and velocity vectors?

Acceleration and velocity vectors are both quantities that describe the motion of an object. Velocity is a vector that describes the rate of change of an object's position with respect to time, while acceleration is a vector that describes the rate of change of an object's velocity with respect to time. In simpler terms, velocity tells us how fast an object is moving and in what direction, while acceleration tells us how much an object's velocity is changing and in what direction.

2. How are acceleration and velocity vectors related?

Acceleration and velocity vectors are related in that acceleration is the derivative of velocity with respect to time. This means that acceleration is the rate of change of velocity with respect to time. This relationship is described by the equation a = dv/dt, where a is acceleration, v is velocity, and t is time.

3. What do the different components of an acceleration/velocity vector represent?

In a two-dimensional motion, the components of an acceleration/velocity vector represent the magnitude and direction of the motion in each respective direction. For example, if an object is moving in the x-direction with a velocity of 5 m/s, the x-component of the velocity vector would be 5 m/s. The y-component would be 0, indicating that there is no motion in the y-direction.

4. How do you calculate the magnitude of an acceleration/velocity vector?

The magnitude of an acceleration/velocity vector can be calculated using the Pythagorean theorem. This states that the magnitude of a vector is equal to the square root of the sum of the squares of its components. In other words, for a two-dimensional vector with components x and y, the magnitude can be calculated as sqrt(x^2 + y^2).

5. How do you determine the direction of an acceleration/velocity vector?

The direction of an acceleration/velocity vector can be determined by using trigonometric functions. For a two-dimensional vector with components x and y, the direction can be calculated as the inverse tangent of y/x. This will give you the angle between the vector and the x-axis, which can then be used to determine the direction in terms of a compass direction or degrees.

Similar threads

How Does an Object's Acceleration Affect its Initial Velocity?
Replies
12
Views
7K
Which statement is true? (Velocity and Acceleration of a Tennis Ball)
2
Replies
68
Views
4K
Why Use Unit Vectors in Calculations?
Replies
4
Views
2K
Solving Vector Diagrams: Finding Displacements & Velocities
Replies
5
Views
1K
Mass, acceleration and velocity
Replies
3
Views
1K
Vectors - Aircraft's velocity relative to ground
Replies
2
Views
995
Solve Angular Velocity & Acceleration - Dimensional Analysis
Replies
3
Views
1K
Finding the change in velocity from an acceleration vs time graph
Replies
1
Views
3K
Projectile Motion velocity vector Problem
Replies
2
Views
2K
Acceleration of a Particle Due to Magnetic Field
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top