Starting from rest, a particle moves in a straight line with constant acceleration. After 10 seconds the particle has traveled 200m. What is its acceleration (in m/s2)?

Question

BlackTom AI · Accepted Answer

Consider the kinematics of constant acceleration from rest. For motion with constant acceleration a starting from rest, the displacement after time t is s = (1/2) a t^2.

Plugging in the given values: t = 10 s, s = 200 m, we get 200 = (1/2) a (10)^2 = 50 a.
Solving for a yields a = 200 / 50 = 4 m/s^2.

Option by option analysis:
- Option 4: This matches the calculated acceleration exactly, since 50a = 200 implies a = 4. This aligns with the formula for displacement with constant acceleration from rest.
- Option 40: If a were 40 m/s^2, the displacement would be s = 50 × 40 = 2000 m, not 200 m, so this is inconsistent with the given data.
- Option 7: With a = 7 m/s^2, the displacement would be s = 50 × 7 = 350 m, which contradicts the specified 200 m.
- Option 5.2: Using a = 5.2 m/s^2 gives s = 50 × 5.2 = 260 m, again not matching 200 m.
- Option None of these: Since one option (4) satisfies the equation exactly, this choice is incorrect.

Overall, evaluating the displacement formula against each candidate acceleration reveals that only 4 m/s^2 satisfies the given conditions for motion from rest with constant acceleration over 10 seconds.

2025 Fall PHYS 2205 TR 11:00 - 12:15 _ 89122 2205-Makeup Exam-1- Requires Respondus LockDown Browser

Starting from rest, a particle moves in a straight line with constant acceleration. After 10 seconds the particle has traveled 200m. What is its acceleration (in m/s2)?

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