If an object moves at a non-zero constant acceleration for a certain interval of time, then the distance it covers in that time
- A.depends on its initial velocity.
- B.is independent of its initial velocity.
- C.increases linearly with time.
- D.depends on its initial displacement.
Correct answer
Explanation
The correct answer is A, depends on its initial velocity. With constant acceleration the distance covered is s = ut + ½at², and the first term contains the initial velocity u.
This is the second equation of motion. In a given time t with a given acceleration a, an object that starts faster covers more ground, because the ut term adds the distance it would have covered anyway at its starting speed. A car accelerating from 20 m/s goes much farther in five seconds than the same car accelerating from rest. The other two equations, v = u + at and v² = u² + 2as, also contain u.
B is wrong because the formula shows u directly; only when the object starts from rest does the term vanish.
C is wrong because the ½at² term makes the distance grow with the square of time, not in a straight line.
D is wrong because the distance covered depends on how the object moves, not on where it started from.
Exam tip: s = ut + ½at²; from rest the distance grows as t², so distances in successive equal seconds are in the ratio 1 : 3 : 5 : 7.
Practice Questions
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