Question

The displacement of a body moving along a straight line is given by s=bt^n where b is constant and t is time for whath value of n the body moves under the action of constant force

Answer 1

answer : n = 2

explanation : a/c to question, body moves under the action of constant force.

from Newton's law, F = ma , where m is mass and a is acceleration.

so, if F is constant then a should be constant.

hence, a = constant......(1)

now given expression , s = btⁿ

differentiate both sides with respect to t,

ds/dt = b d(tⁿ)/dt = bnt^(n -1)

again differentiate with respect to t,

d²s/dt² = bn(n - 1)t^(n-2)

we know, acceleration , a = d²s/dt²

so, a = bn(n - 1)t^(n - 2)

but from equation (1), it is clear that Acceleration is constant.

it is possible only if power of t will be zero.

i.e., n - 2 = 0 ⇒ n = 2