Question

The distance x covered by a body moving in a straight line in time t is given by x²=t²+2t+3. The
acceleration of the body will vary as:
a)1/x
b)1/x²
c)1/x³
d)1/x⁴​

Answer 1

answer

c. 1/X^3

Explanation:

x²=t²+2t+3

2xv=2t+2

xv=t+1 ......(i)

x²=(xv)²+2

v²=1-(2/x²)

2v(dv/dx)=-4/x³

a=-2/x³

Hence a is proportional to 1/x³.

Method II

Continuing from i

xa+v²=1

a=(1-v²)/x

a={1-[(t+1)/x]²}/x

a=[x²-(t+1)²]/x³

a=2/x³

a is proportional to 1/x³