Question

The acceleration-time graph of a body is shown below–

The most probable velocity-time graph of the body is

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Answer 2

From given $a - t$ graph acceleration is increasing at constant rate

$\therefore$ $\frac { d a } { d t } = k$ (constant) ⇒ $a = k t$ (by integration)

⇒ $\frac { d v } { d t } = k t$ ⇒ $d v = k t d t$

⇒ $\int d v = k \int t d t$ ⇒ $v = \frac { k t ^ { 2 } } { 2 }$

i.e., v is dependent on time parabolically and parabola is symmetric about v-axis. and suddenly acceleration becomes zero. i.e. velocity becomes constant.

Hence (3) is most probable graph.