Which one of the following equations represents the motion of a body with finite constant acceleration? In these equations, y denotes the displacement of the body at time t and a, b and c are constants of motion.

Question

Which one of the following equations represents the motion of a body with finite constant acceleration? In these equations, y denotes the displacement of the body at time t and a, b and c are constants of motion. (A) y=a t (B) y=a t+b t2 (C) y=a t+b t2+c t3 (D) y=a t-1+b t

Tardigrade Admin · Accepted Answer

y (dy/dt) (d2y/dt2) (a)y = at a 0 (b)y =at +bt2 a +2bt 2b (c)y = at +bt2 +ct3 a + 2bt +3ct2 2b +6ct (d)y = at-1 +bt -at-2 + b 2at-3 Acceleration =(d2 y/d t2) is finite and constant in case (b).

y	$\frac{d y}{d t}$	$\frac{d ^{2} y}{d t ^{2}}$
(a) $y = a t$	a	0
(b) $y = a t + b t^{2}$	a +2bt	2b
(c) $y = a t + b t^{2} + c t^{3}$	$a + 2 b t + 3 c t^{2}$	$2 b + 6 c t$
(d) $y = a t^{- 1} + b t$	$- a t^{- 2} + b$	$2 a t^{- 3}$

Q. Which one of the following equations represents the motion of a body with finite constant acceleration? In these equations, y denotes the displacement of the body at time t and a,b and c are constants of motion.

y=at

y=at+bt2

y=at+bt2+ct3

y=at−1+bt

y dtdy​ dt2d2y​ (a)y=at a 0 (b)y=at+bt2 a +2bt 2b (c)y=at+bt2+ct3 a+2bt+3ct2 2b+6ct (d)y=at−1+bt −at−2+b 2at−3 Acceleration =dt2d2y​ is finite and constant in case (b).

Q. Which one of the following equations represents the motion of a body with finite constant acceleration? In these equations, $y$ denotes the displacement of the body at time $t$ and $a, b$ and $c$ are constants of motion.

$y = a t$

$y = a t + b t^{2}$

$y = a t + b t^{2} + c t^{3}$

$y = a t^{- 1} + b t$