Question: 41: The position-time \left(\mathrm{x}-\mathrm{t}\right) graph for positive acceleration is :
Answer: Option (1)
Explanation:
Acceleration is defined as the rate of change of velocity with respect to time.
Velocity is the slope of the position-time graph and is given by \mathrm{v}=\frac{dx}{dt}.
Positive acceleration means velocity increases with time,
so the slope of the \mathrm{x}-\mathrm{t} graph must increase continuously.
This implies that the position-time graph should be a curve that becomes steeper with time,
i.e., it is concave upward.
In option (1), the slope of the graph increases as time increases, indicating increasing velocity
and hence positive acceleration.
Option (2) shows decreasing slope with time, which corresponds to negative acceleration.
Option (3) is a straight line with constant slope, indicating constant velocity and zero acceleration.
Option (4) shows a negative slope, indicating motion with negative velocity.
Therefore, the correct position-time graph for positive acceleration is option (1).