Question

A particle moves along Y-axis in such a way that its y-coordinate varies with time $t$ according to the relation $y = 3 +5t + 7t ^2$. The initial velocity and acceleration of the particle are respectively

• A. $14 m$ $s^{-1}, -5m\,s^{-2}$
• B. $19 m$ $s^{-1}$,$-9\,m$ $s^{-2}$
• C. $-14\, m$ $s^{-1}$,$-5\,m$ $s^{-2}$
• D. $5 \,m$ $s^{-1}$,$14\,m$ $s^{-2}$

Answer 1

Answer: (D)

$5 \,m$ $s^{-1}$,$14\,m$ $s^{-2}$

Answer 2

Given $y = 3 + 5t+7t^2$
Velocity (v) is defined as rate of change of displacement, also
using $\frac{d}{dx}x^n=nx^{n-1},$ we have
hence $v=\frac{dy}{dt}=5+15t$
Initial velocity at t = 0, is
$v=5ms^{-1}$
Also acceleration a =$\frac{d^2 y}{dt^2}$
$=14 ms^{-2}$