The acceleration of a particle is increasing linearly with time t as bt. The particle starts from origin with an initial velocity v₀. The distance travelled by the particle in time t will be (a) v₀ t + 1/3bt² (b) v₀ t + 1/2bt² (c) v₀ t + 1/6bt³ (d) v₀ t + 1/3bt³

Answer: (c). a = bt ⇒ v = v₀ + bt²/2 x = ∫₀t v dt = v₀ t + bt³/6 So the answer is (c) v₀ t + 1/6bt³.

The acceleration of a particle is increasing linearly with time t as… | NEET 1995 (AIPMT)

Q49NEET 1995 · AIPMTMedium

Velocity, Acceleration & Variable Motion

The acceleration of a particle is increasing linearly with time $t$ as $bt$ . The particle starts from origin with an initial velocity $v_0$ . The distance travelled by the particle in time $t$ will be

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Answer: (c)

$a = bt \Rightarrow v = v_0 + \dfrac{bt^2}{2}$
$x = \int_0^t v\,dt = v_0 t + \dfrac{bt^3}{6}$
So the answer is (c) $v_0 t + \dfrac{1}{6}bt^3$ .

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Velocity, Acceleration & Variable Motion question from NEET 1995 (AIPMT)

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