Question

question 9
ch question has four options among which only one of them is correct.
which of the following graphs represents the motion of a car moving on a straight with constant acceleration? ( ).
(a)
(b)
(c)
(d)

Explanation:

Step1: Recall acceleration definition

Acceleration \( a = \frac{\Delta v}{\Delta t} \). For constant acceleration, if acceleration is non - zero, velocity \( v \) should change linearly with time \( t \) (since \( a=\text{constant}=\frac{v - v_0}{t - t_0} \), so \( v=v_0+at \), a linear equation). For position - time (\( x - t \)) graphs, the slope is velocity (\( v=\frac{\Delta x}{\Delta t} \)).

Step2: Analyze Option A

In option A, the \( v - t \) graph is a horizontal line. This means \( \Delta v = 0 \) over time, so acceleration \( a=\frac{\Delta v}{\Delta t}=0 \) (uniform motion, not constant non - zero acceleration).

Step3: Analyze Option B

In option B, the \( x - t \) graph is a straight line through the origin. The slope of an \( x - t \) graph is velocity. A straight line with constant slope means constant velocity (\( v=\text{constant} \)), so acceleration \( a = \frac{\Delta v}{\Delta t}=0 \) (uniform motion, not constant non - zero acceleration).

Step4: Analyze Option C

In option C, the \( x - t \) graph is a straight line with negative slope. The slope is constant, so velocity is constant (negative constant velocity), and acceleration \( a=\frac{\Delta v}{\Delta t}=0 \) (uniform motion, not constant non - zero acceleration).

Step5: Analyze Option D

In option D, the \( v - t \) graph is a straight line passing through the origin. The slope of a \( v - t \) graph is acceleration (\( a=\frac{\Delta v}{\Delta t} \)). Since it's a straight line, the slope (acceleration) is constant. This represents motion with constant acceleration (if initial velocity \( v_0 = 0 \), \( v=at \), which is a linear relationship between \( v \) and \( t \)).

Answer:

D. The \( v - t \) graph in option D is a straight line, meaning acceleration (slope of \( v - t \) graph) is constant, while other options represent motion with zero acceleration (uniform motion).