Question

In the rectilinear motion of a point, the time t and
position x satisfy the equation
t= ax + bx + c (a, b, c are constants) velocity
in the position x is
(1) (2ax + b)^-1
(2) 1/(2ax+b)^2
(3) x^2
(4) 1/(ax+b)^2
​

Answer 1

Answer: (2ax+b)^-1

Explanation: always use chain rule during differentiation

Answer 2

Answer:

(2ax+b)^-1 will be proportional to velocity.

Explanation:

Since we know the equation from the question which is t= ax^2 + bx + c so to get velocity we know that rate of change of distance with time is velocity which is differntiation of x with respect to t.

So, d/dt of the entire equation will be

1=2axdx/dt + bdx/dt + 0 hence on solving it we will get 1/(2ax+b) will be equal to dx/dt. So again dx/dt is (2ax+b)^-1.