Displacement of a Rolling Ball with Initial Velocity and Constant Acceleration

In summary, the ball rolling with an initial velocity of 40m/s[W] undergoes an acceleration of 5.0m/s2[N] for a period of 6.0 seconds, resulting in a displacement of 260m[W21°N] in that time. The formula V22 = V12 + 2ad can be used to calculate the displacement, taking into account both the direction and magnitude of acceleration. It is also possible to calculate the displacement separately for the x and y directions and then combine them using vector addition.
  • #1
physics.
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Homework Statement


A ball rolling with an initial velocity of 40m/s[W] undergoes an acceleration of 5.0m/s2[N] for a period of 6.0 seconds. What is the displacement of the ball in the 6.0 seconds?

The Attempt at a Solution



Apparently the answer is 260m[W21°N]

Please help!
 
Last edited:
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  • #2
PF rule. No attempt means no help.
 
  • #3
Do you not know any formulas relating constant acceleration to speed and distance?
 
  • #4
Well I know the displacement north is 30m, because i was given an acceleration and a time. From that I found the final velocity of 50m/s from the triangle these two velocities created. Using the motion formula V22 = V12 + 2ad , i found the displacement to be 90, not 260... And I have no idea how to use vectors in this case to find a direction
 
  • #5
physics. said:
Well I know the displacement north is 30m, because i was given an acceleration and a time. From that I found the final velocity of 50m/s from the triangle these two velocities created. Using the motion formula V22 = V12 + 2ad , i found the displacement to be 90, not 260... And I have no idea how to use vectors in this case to find a direction

You have to use vectors in this case. Or just find the x-direction motion separately and y-direction displacement separately. Then add those two Vectorially by forming triangle as you did to final velocity. Hope you find this helpful.
 

Related to Displacement of a Rolling Ball with Initial Velocity and Constant Acceleration

1. What is the difference between 1D and 2D motion?

1D motion refers to motion that only occurs along a straight line, while 2D motion involves movement in two perpendicular directions, typically represented by the x and y axes.

2. How do you calculate displacement in 1D and 2D motion?

In 1D motion, displacement is simply the difference between the final and initial position of the object. In 2D motion, displacement can be calculated using the Pythagorean theorem, where the displacement is the square root of the sum of the squares of the x and y displacements.

3. What is the equation for average velocity in 1D and 2D motion?

In 1D motion, average velocity is calculated by dividing the total displacement by the total time. In 2D motion, average velocity is calculated by dividing the total displacement in the x and y directions by the total time.

4. How does acceleration affect 1D and 2D motion?

In 1D motion, acceleration can change the speed or direction of an object's motion. In 2D motion, acceleration can change the speed or direction of an object's motion in both the x and y directions.

5. What are some real-life examples of 1D and 2D motion?

1D motion can occur when a car travels along a straight road or when a pendulum swings back and forth. 2D motion can be seen when a ball is thrown in the air, when a plane flies in the sky, or when a person walks in a zigzag pattern.

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