Assertion: If $α$ = $-$ 2t for a particle moving in a straight line starting with initial velocity 4 m/s from the origin, then distance travelled by it in 2 s is same as displacement.
Reason: Velocity changes direction after 2 s only.

If both assertion and reason are true and reason is the correct explanation of assertion.

If both assertion and reason are true but reason is not the correct explanation of assertion.

If assertion is true but reason is false.

If both assertion and reason are false.

Solution

If both assertion and reason are true but reason is not the correct explanation of assertion.

Acceleration is given by

$α$ = $-$ 2t

$\frac{dv}{dt} = -$ 2t

⇒ $\int_{4}^{v}$ dv = $- \int_{0}^{t}$ t dt

⇒ ${[v]}_{4}^{v}$ = $- {[t]}_{0}^{t}$

⇒ v $-$ 4 = $-$ t²

⇒ v = 4 $-$ t²

⇒ v > 0 for t < 2

v = 0 for t = 2

v < 0 for t > 2

The body reverses its direction of motion after 2 s.

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