For which of the following position-time (x-t) graphs is acceleration zero?

Step 1: Acceleration is zero when velocity is constant. In an $x$-$t$ graph, constant velocity appears as a straight line (non-zero slope).

Observe the graphs: Graph (A) is a straight line (constant slope), so acceleration is zero throughout.

Graphs (B), (C), (D) are curved or piecewise, indicating changing velocity.

Answer for Q12: (A)

Step 1: Maximum velocity from $v$-$t$ graph is the highest $v$ value (peak ordinate).

Step 2: Maximum displacement is the maximum area under $v$-$t$ curve up to that point ($\max \int v \, dt$).

Step 3: Maximum acceleration is the maximum slope of $v$-$t$ graph ($\max \frac{\Delta v}{\Delta t}$).

Step 4: Average displacement is total area under curve divided by time interval ($\frac{1}{T} \int_0^T v \, dt$).

(Specific values require graph scales; read from given $v$-$t$ graphs for A, B, C, D.)

The area under $v$-$t$ graph represents displacement ($\int v \, dt = \Delta x$), not velocity or acceleration.

Velocity = ordinate value. Acceleration = slope.

neither (A) nor (B); it is displacement