Physics · Motion In A Straight Line · NEET
The slope gives the acceleration. Slope = (change in velocity) / (change in time) = (v2 - v1)/(t2 - t1), which is exactly the definition of acceleration a. A steeper line means larger acceleration. A flat (horizontal) line means slope = 0, so acceleration = 0 (constant velocity). NCERT states it clearly: 'the acceleration of an object at a particular time is the slope of the velocity-time graph at that instant.'
The area between the v-t line and the time axis gives the displacement in that time interval. NCERT proves this for constant velocity u: the graph is a flat line, and the area under it from t = 0 to t = T is a rectangle of height u and base T, so area = u × T = uT, which is exactly the displacement. For a slanted line you get a triangle or a trapezium — same idea, just compute that area.
They look similar but mean opposite things. On an x-t graph the slope gives VELOCITY. On a v-t graph the slope gives ACCELERATION, and the AREA gives displacement. So a straight slanted line on an x-t graph means constant velocity, but a straight slanted line on a v-t graph means constant acceleration (velocity is changing steadily).
A horizontal line means velocity is not changing. Slope = 0, so acceleration = 0. The body moves with constant (uniform) velocity. If the flat line is above the time axis the body moves in the positive direction; if below, in the negative direction.
At the crossing point the velocity is zero, meaning the body momentarily stops. After crossing, velocity changes sign, so the body reverses direction. Classic example: a ball thrown straight up — v starts positive, decreases to 0 at the top, then becomes negative as it falls. The v-t graph is one straight line of slope -g that crosses the time axis at the highest point.
Look at the direction the line tilts. A line going UP to the right has a positive slope, so acceleration is positive (speeding up if moving in the positive direction). A line going DOWN to the right has a negative slope, so acceleration is negative (this is retardation if the body is moving in the positive direction). A flat line means zero acceleration.
The velocity (v)-time (t) graph of a body moving in a straight line is shown. Which of the following acceleration (a)-time (t) graphs best represents the motion?
A ball is thrown vertically upward and falls back to the thrower. Which velocity (v)-time (t) graph correctly represents its motion? (upward taken positive)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Because velocity × time = displacement. On a v-t graph, height is velocity and base is time, so the area (height × base) has units of velocity × time = metres, which is displacement. The slope, on the other hand, is velocity ÷ time = acceleration. Different operations give different quantities.
It gives displacement. If part of the graph is below the time axis (velocity negative), that area is counted as negative. To get total distance travelled instead, add the areas as positive (ignore the sign).
A straight slanted line. Since acceleration is constant, the slope is constant, so the line is straight. If acceleration is zero (uniform velocity) the line is horizontal; if acceleration changes, the line becomes a curve.
No. A vertical line would mean the velocity has many values at the same instant of time, which is physically impossible. A body has only one velocity at any given instant.
Motion in a Straight Line is a scoring chapter and NEET regularly asks graph-matching questions (v-t to a-t, or identifying the correct v-t for thrown-up motion). Knowing 'slope = acceleration, area = displacement' lets you answer these in seconds without any long calculation.
