Question

which of the following graphs represents the motion of a car moving on a straight with constant acceleration? ( ). (a) v-t graph with horizontal line (b) x-t graph with straight line through origin (c) x-t graph with straight line decreasing from y-intercept to origin (d) v-t graph with straight line through origin increasing

Explanation:

Step1: Analyze Option A

In a velocity - time ($v - t$) graph, the slope of the graph represents acceleration ($a=\frac{\Delta v}{\Delta t}$). For option A, the velocity - time graph is a horizontal line, which means $\Delta v = 0$ over time. So the acceleration $a=\frac{\Delta v}{\Delta t}=0$, which is motion with constant velocity (uniform motion), not constant non - zero acceleration.

Step2: Analyze Option B

In a position - time ($x - t$) graph, the slope of the graph represents velocity ($v=\frac{\Delta x}{\Delta t}$). For option B, the position - time graph is a straight line passing through the origin, so the slope (velocity) is constant. If velocity is constant, then acceleration $a=\frac{\Delta v}{\Delta t}=0$, which is uniform motion, not motion with constant acceleration.

Step3: Analyze Option C

In a position - time ($x - t$) graph, the slope of the graph represents velocity. For option C, the position - time graph is a straight line with a negative slope, so the velocity is constant (since the slope is constant). If velocity is constant, then acceleration $a = 0$, which is uniform motion, not motion with constant acceleration.

Step4: Analyze Option D

In a velocity - time ($v - t$) graph, the slope of the graph represents acceleration. For option D, the velocity - time graph is a straight line passing through the origin, so the slope (acceleration) is constant (because the graph has a constant slope). This represents motion with constant acceleration.

Answer:

D. The graph in option D (a velocity - time graph with a straight line passing through the origin) represents the motion of a car moving on a straight line with constant acceleration, as the slope of a velocity - time graph gives acceleration and a constant slope implies constant acceleration.