Distance-Time Graph for Constant Acceleration – Rankers Physics

Graphs of Motion: Practice Problem & Solution

Assertion (A): For motion from rest with constant acceleration distance time graph is a parabola, always with increasing slope. Reason (R): Speed of the body starting from rest with constant acceleration always increases linearly with time.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Graphs of Motion. Understanding the underlying formula is key to arriving at the correct answer below:

Formula: For (u=0), \(s = \frac{1}{2}at^2\) and (v = at).
Solution: (A) is true; \(s = \frac{1}{2}at^2\) is a parabola, and its slope (velocity (v=at)) increases with time. (R) is true; (v=at) shows speed increases linearly from rest. (R) correctly explains (A) because the linearly increasing speed implies an increasing slope for the distance-time graph.

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