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

Answer 1

Answer: (B)

$a=-2t$
$\frac{dv}{dt}=-2t\,or\,\int^{^v}_{_4}dv=-2\int^{t}_{0}\,t\,dt$
$v-4=-t^{2}$ or $v=4-t^{2}$
$\Rightarrow \quad v>0\,for\,t<2,$
$\quad\quad v=0\,for\,t=2,$
$\quad\quad v<0\,for\,t>2$
The body reverses its direction of motion after 2 s.