Physics · Motion In A Straight Line · NEET
On an x-t graph, the vertical axis is position (x) and the horizontal axis is time (t). Slope is defined as rise over run = change in x divided by change in t = Δx/Δt. But Δx/Δt is the definition of velocity itself. So the slope is not just linked to velocity - it IS velocity. There is no extra formula to memorise; slope and velocity are the same ratio.
Steeper means faster. A steep line covers a large change in position (large Δx) in a small change in time (small Δt), so Δx/Δt is big, meaning high velocity. A nearly flat line covers little distance over lots of time, so velocity is small. This is the fastest way to compare two bodies on the same graph - just look at which line is steeper.
A horizontal line means position is not changing as time passes, so Δx = 0. Then slope = 0/Δt = 0, so velocity = 0. The object is at rest. Students often think a flat line means constant speed - it does not; flat means stopped. A tilted straight line is the one that means constant (non-zero) velocity.
For a straight-line (linear) x-t graph the slope is the same everywhere, so average velocity and instantaneous velocity are equal. For a curved x-t graph, the slope of the straight line joining two points gives average velocity, while the slope of the tangent at a single point gives instantaneous velocity, v = dx/dt. NEET tests both, so read whether the graph is a straight line or a curve.
A negative slope (line going downward as time increases) means position is decreasing, so the object is moving in the negative direction (back toward or past the origin). The velocity is negative. The steepness still tells you the magnitude of speed; the sign only tells you the direction.
The displacement-time (x-t) graphs of two moving particles make angles of 30 degrees and 45 degrees with the time axis. The ratio of their respective velocities v1 : v2 is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is equal to velocity. Slope = Δx/Δt = displacement/time, which is exactly the definition of velocity. Units of the slope are metres per second (m/s).
Draw a tangent to the curve at the point of interest and find the slope of that tangent line. That slope is the instantaneous velocity, v = dx/dt, at that instant.
Zero slope (a horizontal line) means the velocity is zero, so the body is at rest during that time interval.
Yes. A downward line has negative slope, meaning negative velocity - the object moves in the negative direction. The steepness still gives the speed's magnitude.
Because a steeper line has a larger Δx for the same Δt, so Δx/Δt (velocity) is larger. On one graph, the steepest line is always the fastest body.
