A particle is moving with constant acceleration 'a'. Following graph shows v² versus x(displacement) plot. The acceleration of the particle is ___________ m/s².

Solution

Physics sir · 3 steps

A straight line on a v² versus x graph means its slope is 2a, so read the slope and halve it.

1. Pick the equation. For constant acceleration, v² = u² + 2ax. Plotting v² against x gives a straight line with intercept u² and slope 2a.

   slope = (Δ (v²))/(Δ x) = 2a

2. Read the slope. From point A (10, 40) to point C (30, 80): slope = (80 - 40)/(30 - 10) = 40/20 = 2 m s⁻². The intercept at x = 0 is 20, so u² = 20 m² s⁻², which fits the same line.
3. So. 2a = 2, so a = 1 m s⁻².

The common slip: 2. Taking the slope itself as the acceleration gives 2, not 1. The slope of this graph is 2a.

The idea to keep. On a v² versus x graph, the slope is 2a and the intercept is u². Always halve the slope to get the acceleration.

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