The displacement of a particle moving in a straight line is given by the expression x=A t3+B t2+C t+D in metres, where t is in seconds and A, B, C and D are constants. The ratio between the initial acceleration and initial velocity is

Question

The displacement of a particle moving in a straight line is given by the expression x=A t3+B t2+C t+D in metres, where t is in seconds and A, B, C and D are constants. The ratio between the initial acceleration and initial velocity is (A) (2 C/B) (B) (2 B/C) (C) 2 barC (D) (C/2 B)

Tardigrade Admin · Accepted Answer

Displacement of a particle moving in a straight

line (x) = A t^{3} + B t^{2} + Ct + D

∴ Velocity, v = \frac{d x}{d t} = 3 A t^{2} + 2 Bt + C

V_{initial} = C

and

a = \frac{d ^{2} x}{d t ^{2}} = 6 A t + 2 B

a_{initial} = 2 B

∴

Ratio between initial acceleration and initial velocity is

\frac{2 B}{C}

Q. The displacement of a particle moving in a straight line is given by the expression $x = A t^{3} + B t^{2} + Ct + D$ in metres, where $t$ is in seconds and $A, B, C$ and $D$ are constants. The ratio between the initial acceleration and initial velocity is

$\frac{2 C}{B}$

$\frac{2 B}{C}$

$2 \overset{ˉ}{C}$

$\frac{C}{2 B}$

Q. The displacement of a particle moving in a straight line is given by the expression x=At3+Bt2+Ct+D in metres, where t is in seconds and A,B,C and D are constants. The ratio between the initial acceleration and initial velocity is

B2C​

C2B​

2Cˉ

2BC​

Displacement of a particle moving in a straight line(x)=At3+Bt2+Ct+D ∴ Velocity, v=dtdx​=3At2+2Bt+C Vinitial ​=C and a=dt2d2x​=6At+2B ainitial ​=2B ∴ Ratio between initial acceleration and initial velocity is C2B​

Q. The displacement of a particle moving in a straight line is given by the expression $x = A t^{3} + B t^{2} + Ct + D$ in metres, where $t$ is in seconds and $A, B, C$ and $D$ are constants. The ratio between the initial acceleration and initial velocity is

$\frac{2 C}{B}$

$\frac{2 B}{C}$

$2 \overset{ˉ}{C}$

$\frac{C}{2 B}$