Compare and contrast the effects of the following changes in motion. Linear acceleration of an object in the direction of motion over 10 seconds at 3 m/s². Centripetal acceleration of an object in motion over 10 seconds at 3 m/s². (1 point) Responses The acceleration vectors are identical because they have the same direction. The acceleration vectors are identical because they have the same direction. - no response given The acceleration vectors are identical because they have the same magnitude. The acceleration vectors are identical because they have the same magnitude. - incorrect The first increases the speed of the object in the direction of motion. The second does not change the object’s speed but will cause it to turn along a circular path. The first increases the speed of the object in the direction of motion. The second does not change the object’s speed but will cause it to turn along a circular path. - no response given The first increases the speed of the object in the direction of motion. The second increases the object’s speed while also changing its direction.

Answer 1

The correct response is: The first increases the speed of the object in the direction of motion. The second does not change the object’s speed but will cause it to turn along a circular path.

Comparison of Effects:

1. Linear Acceleration:

   • Direction: The acceleration is in the same direction as the motion of the object.
   • Effect on Speed: Linear acceleration (3 m/s² over 10 seconds) will increase the object's speed. Using the formula \( v = u + at \), if we assume the initial speed (u) is 0, the final speed would be \( 0 + (3 , \text{m/s}^2 \times 10 , \text{s}) = 30 , \text{m/s} \).
   • Path: The object continues in a straight line while its speed increases.

2. Centripetal Acceleration:

   • Direction: The centripetal acceleration is directed towards the center of the circular path.
   • Effect on Speed: While the magnitude of centripetal acceleration (3 m/s²) maintains the object's current speed, it does not increase it. The object moves at a constant speed while changing direction.
   • Path: The object will follow a circular path, with its direction constantly changing due to the centripetal force acting on it.

Summary:

The key difference is that linear acceleration increases the object's speed in the direction of motion, while centripetal acceleration keeps the object's speed constant but changes its direction, resulting in circular motion.