Question

The relation between time t and distance x is t = ax² + bx where a and bare constants. The acceleration is ______.

पर्याय

• 2bv³

• -2abv²

• 2av²

• -2av³

Answer 1

The relation between time t and distance x is t = ax² + bx where a and bare constants. The acceleration is -2av³.

Explanation:

Given, t = ax² + bx;

Diff. with respect to time (t)

`"d"/"dt"("t")="ad"/"dt"(x^2)+"b"("d"x)/"dt"`

= `"a".2x("d"x)/"dt"+"b"."v"`

⇒ 1 = 2axv + bv = v(2ax + b) (v = velocity)

2ax + b = `1/"v"`

Again differentiating, we get

`2"a"("d"x)/"dt"+0 =-1/"v"^2"dv"`

⇒ a = `"dv"/"dt" = -2"av"^3`     `(∵ ("d"x)/"dt" = "v")`