2-D Kinematic Velocity and Acceleration Practice Problem

• Panda1321
In summary, the dog running in an open field has a velocity of vx = 1.8 m/s and vy = -1.8 m/s at time t1 = 10.8 s. The average acceleration of the dog from t1 = 10.8 s to t2 = 23.2 s has a magnitude of 0.45 m/s2 and a direction of 32.0 ∘ measured from the +x-axis toward the +y-axis. In order to find the x-component of the dog's velocity at t2 = 23.2 s, you need to account for the initial velocity and the fact that the acceleration did not start at t = 0.
Panda1321
"A dog running in an open field has components of velocity vx = 1.8 m/s and vy = -1.8 m/s at time t1 = 10.8 s . For the time interval from t1 = 10.8 s to t2 = 23.2 s , the average acceleration of the dog has magnitude 0.45 m/s2 and direction 32.0 ∘ measured from the +x−axis toward the +y−axis."

A. "At time t2 = 23.2 s , what is the x-component of the dog's velocity?"

Equations:
Vx= dx/dt Vy= dy/dt First, I tried to find the velocity at t2=23.2s by: V=at V=(0.45m/s^2)(23.2s)=10.44m/s
Therefore Vx=10.44m/s

However, this answer is incorrect and I am unable to understand how to find Vx with the data given. Can someone please explain how to solve this problem and if the magnitude and direction given from T1 to T2 is different than the angle formed by starting at the origin to T1? Thanks!

You have assumed that the acceleration is completely in the x direction. According to the problem statement, this is not true.

Edit: Furthermore, you are not accounting for the initial velocity or the fact that the acceleration did not start at t=0.

Panda1321
Panda1321 said:
First, I tried to find the velocity at t2=23.2s by: V=at V=(0.45m/s^2)(23.2s)=10.44m/s
Therefore Vx=10.44m/s

However, this answer is incorrect and I am unable to understand how to find Vx with the data given. Can someone please explain how to solve this problem and if the magnitude and direction given from T1 to T2 is different than the angle formed by starting at the origin to T1? Thanks!
There are several problems. As @Orodruin said you need to work with both the x and y components of velocity.

You also forgot about the initial velocity. Remember the 1-d motion equation is ##v=v_{0}+at##.

Finally the acceleration is not for the entire 23.2s as you have used it. The dog only accelerates for some of that time.

Panda1321

1. What is 2-D kinematics?

2-D kinematics is the study of motion in two dimensions, including both horizontal and vertical components. It involves analyzing the velocity and acceleration of an object in two perpendicular directions.

2. How is velocity calculated in 2-D kinematics?

In 2-D kinematics, velocity is calculated by dividing the displacement in each direction by the corresponding time interval. The final velocity is then the vector sum of the horizontal and vertical components.

3. What is the difference between speed and velocity in 2-D kinematics?

Speed is a scalar quantity that represents the rate of change of distance with time. Velocity, on the other hand, is a vector quantity that includes both the speed and direction of an object's motion.

4. How can acceleration be determined in 2-D kinematics?

Acceleration can be determined by dividing the change in velocity in each direction by the corresponding time interval. The final acceleration is then the vector sum of the horizontal and vertical components.

5. How can 2-D kinematics be applied in real-world situations?

2-D kinematics is used in many real-world situations, such as analyzing the motion of projectiles, understanding the movement of objects in sports, and predicting the path of objects in a two-dimensional plane. It is also important in fields such as engineering, physics, and astronomy.

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