Acceleration Transitional Reasoning Practice

Questions

1. 1.

   During a motion investigation along a straight track, a motorized cart starts from rest with a constant acceleration of $4.0\text{ m/s}^2$. A student records that the cart travels 2.0 m during the first second, 6.0 m during the second second, and 10.0 m during the third second. The student claims that because the cart covers progressively greater distances each second, its acceleration must be increasing. Which statement correctly evaluates the student's claim?

   • A) The claim is valid because an object moving with constant acceleration must travel equal distances during equal time intervals.
   • B) The claim is invalid because a constant acceleration steadily increases the cart's velocity, causing it to cover greater distances in each successive second.
   • C) The claim is valid because the ratio of displacement to elapsed time squared increases between consecutive one-second intervals.
   • D) The claim is invalid because the cart's acceleration must be decreasing whenever displacement increases along the direction of motion.
2. 2.

   A telemetry system monitors two automated test pods, Pod X and Pod Y, moving in the positive direction along parallel straight tracks. Over an identical 2.0-second interval, Pod X increases its velocity from 24 m/s to 30 m/s, while Pod Y increases its velocity from 4.0 m/s to 16 m/s. Based on this motion data, which statement correctly compares and explains the average accelerations of the two pods?

   • A) Pod X has a greater acceleration than Pod Y because its average velocity during the interval is considerably higher.
   • B) Pod X and Pod Y experience the same acceleration because both pods are speeding up under positive forward thrust.
   • C) Pod Y has twice the acceleration of Pod X because acceleration depends on the rate of change in velocity rather than the magnitude of velocity.
   • D) Pod Y has half the acceleration of Pod X because its initial velocity is substantially smaller than that of Pod X.
3. 3.

   An automated cart moves along a straight rail where the positive direction is defined toward the east. A motion sensor records that during a 3.0-second interval, the cart travels west while its speed decreases from 15 m/s to 6 m/s. Which option correctly identifies the direction of the cart's average acceleration and the relationship between its velocity and acceleration vectors during this interval?

   • A) The acceleration is directed west, and the velocity and acceleration vectors point in the same direction.
   • B) The acceleration is directed west, and the velocity and acceleration vectors point in opposite directions.
   • C) The acceleration is directed east, and the velocity and acceleration vectors point in opposite directions.
   • D) The acceleration is directed east, and the velocity and acceleration vectors point in the same direction.
4. 4.

   During a performance test along a straight track, an electric car accelerates from rest to 30 m/s in 6.0 s. Immediately afterward, the driver applies the brakes to avoid an obstacle, slowing the car from 30 m/s to 10 m/s over an interval of 5.0 s. How do the magnitude and direction of the car's acceleration during braking compare with its acceleration during the initial speeding-up phase?

   • A) The braking acceleration has a greater magnitude and acts in the same direction as the initial acceleration.
   • B) The braking acceleration has a smaller magnitude and acts in the opposite direction to the initial acceleration.
   • C) The braking acceleration has a smaller magnitude and acts in the same direction as the initial acceleration.
   • D) The braking acceleration has a greater magnitude and acts in the opposite direction to the initial acceleration.
5. 5.

   An automated inspection cart travels along a straight track with an initial velocity of 18 m/s directed east. To change course, the cart applies its control system and reaches a velocity of 6.0 m/s directed west after an elapsed time of 4.0 seconds. What is the average acceleration of the cart during this 4.0-second interval?

   • A) $3.0\text{ m/s}^2$ directed toward the west
   • B) $3.0\text{ m/s}^2$ directed toward the east
   • C) $6.0\text{ m/s}^2$ directed toward the east
   • D) $6.0\text{ m/s}^2$ directed toward the west

Answers and step-by-step solutions appear after you finish the test.