The velocity-displacement graph describing the motion of bicycle is shown in the figure.
The acceleration-displacement graph of the bicycle's motion is best described by :

Solution

Physics sir · 4 steps

On a v–x graph, acceleration is velocity times the slope, not the slope alone.

1. Acceleration from v–x. With velocity given against displacement, use the chain rule: a = dv/dt = dv/dx × dx/dt. So acceleration is the slope of the graph multiplied by the velocity at that point.

   a = v dv/dx

2. First 200 m. The line goes from 10 to 50 m s⁻¹, so dv/dx = 40/200 = 0.2 s⁻¹ and v = 10 + 0.2x. Then a = 0.2v = 2 + 0.04x, which is a straight line in x that starts at a = 2 m s⁻².
3. Next 200 m. The velocity stays at 50 m s⁻¹, so dv/dx = 0 and a = 0. The graph must drop to zero and run along the x-axis.

   Option	0 to 200 m	200 to 400 m	Matches?
   (a)	straight line rising from 2	zero	yes
   (b)	curve	zero	no
   (c)	curve	constant, not zero	no
   (d)	straight line rising from 2	constant, not zero	no

4. So. Only (a) has the right shape: linear from 2 m s⁻², then zero. With the numbers in the graph, the value at 200 m works out to 0.2 × 50 = 10 m s⁻², not the 18 printed on every option, so judge the options by their shape.

The idea to keep. For any v–x graph use a = v dv/dx. A straight v–x line gives a linear a–x line, and wherever v is constant, the acceleration is zero.

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