NEET2026PhysicsChapterActual
The velocity ( v ) versus time ( t ) graph of a particle moving in a straight line is shown in the figure. The graph consists of three distinct continuous segments: a parabolic curve opening upwards from t = 0 to t = t₁ , a straight line with a positive slope from t = t₁ to t = t₂ , and a horizontal line from t = t₂ to t = t₃ . Which of the following statements correctly describes the acceleration ( a ) of the partic
Options
- AFrom 0 to t₁ , a is a positive constant; from t₁ to t₂ , a increases linearly; from t₂ to t₃ , a is zero.
- BFrom 0 to t₁ , a increases linearly with time; from t₁ to t₂ , a is zero; from t₂ to t₃ , a is a negative cons
- CFrom 0 to t₁ , a increases linearly with time; from t₁ to t₂ , a is a positive constant; from t₂ to t₃ , a is
- DFrom 0 to t₁ , a is a positive constant; from t₁ to t₂ , a is a positive constant; from t₂ to t₃ , a is zero.
Correct answer
C. From 0 to t₁ , a increases linearly with time; from t₁ to t₂ , a is a positive constant; from t₂ to t₃ , a is
Step-by-step solution
The acceleration a of a particle is given by the slope of its velocity-time graph, a = dv dt . From t = 0 to t = t₁ : The v-t graph is a parabola opening upwards. This implies v is proportional to t^2 , so v = kt^2 for some positive constant k . The acceleration is a = dv dt = 2kt , which means the acceleration increases linearly with time. From t = t₁ to t = t₂ : The v-t graph is a straight line with a positive slope. This implies v = mt + c where m > 0 . The acceleration is a = dv dt = m , which means the acceler