COMEDK · Physics · 3. Motion In One Dimension

A car, starting from rest, accelerates at a rate of \(\beta\) through a distance S, then continues at constant speed for time t and then decelerates at a rate of \(\dfrac{\beta}{2}\) to come to rest. If the total distance travelled is \(10\ S\), then ratio \(\dfrac{S}{t^2}\) is

A \(\dfrac{2\beta}{49}\)
B \(\dfrac{\beta}{49}\)
C \(\dfrac{2\beta}{19}\)
D \(\dfrac{2\beta}{64}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\dfrac{2\beta}{49}\)

Step-by-step Solution

Detailed explanation

Let the maximum speed reached by the car be \(v\). For the first part of the motion, the car accelerates from rest at \(\beta\) over a distance \(S\). Using the equation of kinematics: \(v^2 = 0 + 2\beta S \Rightarrow v = \sqrt{2\beta S}\) For the second part of the motion, the…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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