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Two bodies P and Q are moving with uniform velocity. The slope of the distance-time graph of P is less than the slope of the distance-time graph of Q. Which statement is correct?
P is faster than Q
Q is faster than P
Both have the same speed
P is stationary
Q is faster than P
In a distance-time graph, the speed of an object is represented by the slope of the line. Since the slope of body Q is greater than the slope of body P, it follows that Q travels a greater distance in the same amount of time, making Q faster than P.
In a distance-time graph, the speed of an object is represented by the slope of the line. Since the slope of body Q is greater than the slope of body P, it follows that Q travels a greater distance in the same amount of time, making Q faster than P.
Think of two cars on a road: if car Q covers more distance than car P during the same 10-minute interval, car Q must be moving at a higher speed than car P.
Slope = Speed; Steep = Swift.
v=╬Фt╬ФsтАЛ тАФ definition of speed as the ratio of change in distance to change in time
Slope=tan(╬╕) тАФ relation between the slope of a line and the angle it makes with the horizontal axis
The speed of an object in uniform motion is defined as the rate of change of distance, given by v=dtdsтАЛ. Graphically, this corresponds to the slope (m) of the distance-time plot, where m=tan(╬╕). A steeper line (greater angle with the time axis) indicates a higher value of tan(╬╕), directly corresponding to a higher uniform velocity.
Distance-time graphs for uniform motion are always straight lines.
A horizontal line (slope = 0) represents a body at rest.
A steeper slope indicates higher speed.
Analyzing vehicle performance in physics labs
Interpreting motion profiles in robotics
Uniform velocity implies that acceleration is zero.
Option A is incorrect because P has a lower slope, implying lower speed.
Option C is incorrect because different slopes imply different speeds.
Option D is incorrect because a slope exists, so the body must be moving.
B is correct тАФ Q is faster than P because a steeper slope on a distance-time graph signifies a greater rate of displacement per unit time.
Always check the axes labels; if the graph were velocity-time, the slope would represent acceleration, not speed!
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