Question

Which one of the following equation represents the motion of a body moving with constant finite acceleration? In these equation, y denotes the displacement in time t and p, q and r are constant:
(a) y = (p + qt )(t + pt)
(b) y = p + t/r
(c) y = (p + t) (q + t ) (r + t)
(d) y = $\frac{(p + qt)}{rt}$

Answer 1

answer : option (A)

explanation : acceleration is the rate of change of velocity and velocity is the rate of change of displacement.

means, to find acceleration, differentiate displacement function two times.

i.e., a = d²y/dt²

let's check options.

option (A) : y = (p + qt)(t + pt)

differentiating both sides,

dy/dt = q(t + pt) + (p + qt)(1 + p)

again differentiating both sides,

d²y/dt² = q(1 + p) + q(1 + p) => finite and constant terms

so, option (A) is correct.

option (B) : y = p + t/r

differentiating both sides,

dy/dt = 0 + 1/r

again differentiating both sides,

d²y/dt² = 0 => acceleration is zero

it is incorrect.

option (C) : y = (p + t)(q + t)(r + t) [ it is a cubic polynomial and after twice differentiation, we get d²y/dt² depends on t so, acceleration will be variable. ]

it is also incorrect.

option (D) : y = (p + qt)/(rt) [ it can't be constant because variable term, t is placed at denominator. hence, acceleration will be variable ]

so, it is also incorrect.

Answer 2

hope it helps u dude ❤❤❤❤❤