Assertion: If a = -2t for a particle moving in a straight line starting with an 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.

Question

Assertion: If a = -2t for a particle moving in a straight line starting with an 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. (A) If both assertion and reason are true and reason is the correct explanation of assertion (B) If both assertion and reason are true but reason is not the correct explanation of assertion (C) If assertion is true but reason is false (D) If both assertion and reason are false

Tardigrade Admin · Accepted Answer

a=-2t (dv/dt)=-2t or ∫v4dv=-2∫t0 t dt v-4=-t2 or 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.

Q. Assertion : If a = -2t for a particle moving in a straight line starting with an 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

$a = - 2 t$
$\frac{d v}{d t} = - 2 t or \int_{_{4}}^{^{v}} d v = - 2 \int_{0}^{t} t d t$
$v - 4 = - t^{2}$ or $v = 4 - t^{2}$
$\Rightarrow v > 0 f or t < 2,$
$v = 0 f or t = 2,$
$v < 0 f or t > 2$
The body reverses its direction of motion after 2 s.

Q. Assertion : If a = -2t for a particle moving in a straight line starting with an 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.