Question

The velocity (\( v \))-time (\( t \)) graph for the motion of a body is a straight line making an angle \( 60^\circ \) with the time axis. Then the body is moving with an acceleration (in m\( s^{-2} \)) of:

• A. 1
• B. \(\dfrac{\sqrt{3}}{2}\)
• C. \(\dfrac{1}{\sqrt{3}}\)
• D. \(\sqrt{3}\)
• E. zero

Hint:

In velocity-time graphs, the slope represents acceleration. If the graph is a straight line, simply calculate the slope using the angle with the time axis.

Answer 1

The Correct Option is D

Step 1: The slope of the velocity-time graph represents the acceleration of the body. In this case, the graph is a straight line making an angle of \( 60^\circ \) with the time axis. The slope of the line is given by: \[ \text{Slope} = \tan(\theta) \] where \( \theta = 60^\circ \).

Step 2: The value of \( \tan(60^\circ) \) is known to be \( \sqrt{3} \). Therefore, the acceleration of the body is: \[ \text{Acceleration} = \tan(60^\circ) = \sqrt{3} \]
Step 3: Hence, the body is moving with an acceleration of \( \sqrt{3} \) m/s\( ^2 \). Therefore, the correct answer is option (D).