Two objects, A and B, accelerate from rest at uniform rates. B accelerates twice as much as Compared to A, B travels

The question is incomplete as written. It doesn't say how long the objects accelerate, so I need to fill in the missing part. The usual version of this question reads: "Two objects, A and B, accelerate from rest at uniform rates. B accelerates twice as much as A. Compared to A, B travels ___ in the same time." I'll solve it with that assumption.

Step 1: Concept For an object starting from rest with uniform acceleration, the equation of motion is:

s = ut + ½at²

Since u = 0, this becomes:

s = ½at²

So for the same time t, the distance travelled is directly proportional to the acceleration.

Step 2: Apply to A and B

• A: s_A = ½ a t²
• B: acceleration = 2a, so s_B = ½ (2a) t² = a t²

Step 3: Compare s_B / s_A = (a t²) / (½ a t²) = 2

So B travels two times as far as A in the same time.

Answer: C. two times as far

Note on the assumption: If the question meant the same time, the answer is C, as shown above. If it had meant something else, such as the same distance, the result would differ. The "same time" reading is the standard one and is the only one that fits the options given.

Exam tip: From rest, s = ½at², so for equal times, distance ∝ acceleration. Double the acceleration means double the distance. If the question compared equal distances instead, time would be ∝ 1/√a. Always check which quantity is held constant.