An equation x=t3-2f denotes relationship between displacement and time. At t = 4 s, acceleration is given by:

Question

An equation x=t3-2f denotes relationship between displacement and time. At t = 4 s, acceleration is given by: (A) 12 unit (B) 22 unit (C) 24 unit (D) 26 unit

Tardigrade Admin · Accepted Answer

Rate of change of velocity gives acceleration.
Given,

x = t^{3} - 2 t

Differentiating with respect to

t

,
we get

v = \frac{d x}{d t} = 3 t^{2} - 2

For acceleration

v = \frac{d x}{d t} = \frac{d ^{2} x}{d t ^{2}} = 6 t

Given,

t = 4 s

∴ a = 6 \times 4 = 24 m / s^{2}

Q. An equation x=t3−2f denotes relationship between displacement and time. At t=4s, acceleration is given by:

12 unit

22 unit

24 unit

26 unit

Rate of change of velocity gives acceleration. Given, x=t3−2t Differentiating with respect to t, we get v=dtdx​=3t2−2 For acceleration v=dtdx​=dt2d2x​=6t Given, t=4s ∴a=6×4=24m/s2

Q. An equation $x = t^{3} - 2 f$ denotes relationship between displacement and time. At $t = 4 s$ , acceleration is given by:

Rate of change of velocity gives acceleration.
Given, $x = t^{3} - 2 t$ Differentiating with respect to $t$ ,
we get $v = \frac{d x}{d t} = 3 t^{2} - 2$
For acceleration $v = \frac{d x}{d t} = \frac{d ^{2} x}{d t ^{2}} = 6 t$
Given, $t = 4 s$
$∴ a = 6 \times 4 = 24 m / s^{2}$