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.
Motion in a Straight Line
Solution:
y
$\frac{dy}{dt}$
$\frac{d^2y}{dt^2}$
(a)$y = at$
a
0
(b)$y =at +bt^2$
a +2bt
2b
(c)$y = at +bt^2 +ct^3$
$a + 2bt +3ct^2$
$2b +6ct$
(d)$y = at^{-1} +bt$
$-at^{-2} + b$
$2at^{-3}$
Acceleration $=\frac{d^{2} y}{d t^{2}}$ is finite and constant in case (b).
| y | $\frac{dy}{dt}$ | $\frac{d^2y}{dt^2}$ |
| (a)$y = at$ | a | 0 |
| (b)$y =at +bt^2$ | a +2bt | 2b |
| (c)$y = at +bt^2 +ct^3$ | $a + 2bt +3ct^2$ | $2b +6ct$ |
| (d)$y = at^{-1} +bt$ | $-at^{-2} + b$ | $2at^{-3}$ |