The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :

Solution

Physics sir · 3 steps

Constant a makes v a straight line, and a straight-line v makes x a parabola. Check each panel for that.

1. Build the chain. With constant a, the velocity is v = u + at, a straight line of slope a. The position is x = x₀ + ut + 1/2at², a parabola.
2. Slopes must agree. The slope of the x–t graph is v, and the slope of the v–t graph is a. A positive constant a means v rises steadily, so the x curve keeps getting steeper and bends upward.

   Option	x–t	v–t	Fits constant a > 0?
   (a)	straight line	curve getting steeper	No: a curved v means a changes, and a straight x means v is constant
   (b)	parabola bending upward	straight line rising	Yes
   (c)	straight line	straight line rising	No: a straight x means v is constant, yet v is rising
   (d)	curve bending upward	straight line falling	No: a falling v needs a < 0, but a is drawn positive

3. So. Only (b) has a constant a, a straight-line v and a parabolic x, so the answer is (b).

The idea to keep. Each graph is the slope of the one before it. Constant a gives a straight-line v and a parabolic x. Check that each slope matches the next graph.

Answer from the NTA final answer key. Solution by PrepWiser.