A particle is moving along x -axis with its position (x) varying with time (t) as x=α t^4+β t^2+γ t+ . The ratio of its initial velocity to its initial acceleration, respectively, is:

Correct answer: D. γ: 2 β Position of particle, x=α t^4+β t^2+γ t+ Velocity v=(d x)/(d t)=4 α t^3+2 β t+γ Initial velocity =v(t=0)=γ Acceleration a=(d v)/(d t)=12 α t^2+2 β Initial acceleration =a(t=0)=2 β (v(t=0))/(a(t=0))=(γ)/(2 β)

NEET 2024

Exam: NEET
Year: 2024
Subject: Physics
Chapter: Motion in One Dimension

NEET 2024 · Physics · Motion in One Dimension

A particle is moving along x -axis with its position (x) varying...

A particle is moving along

x

-axis with its position (x) varying with time

(t)

x=\alpha t^4+\beta t^2+\gamma t+\delta

. The ratio of its initial velocity to its initial acceleration, respectively, is:

Options

A $2 \alpha: \delta$
B $\gamma: 2 \delta$
C $4 \alpha: \beta$
D $\gamma: 2 \beta$

Correct answer

D. $\gamma: 2 \beta$

Step-by-step solution

Position of particle,

x=\alpha t^4+\beta t^2+\gamma t+\delta

Velocity

v=\frac{d x}{d t}=4 \alpha t^3+2 \beta t+\gamma

Initial velocity

=v(t=0)=\gamma

Acceleration

a=\frac{d v}{d t}=12 \alpha t^2+2 \beta

Initial acceleration

=a(t=0)=2 \beta

\therefore \frac{v(t=0)}{a(t=0)}=\frac{\gamma}{2 \beta}

Practice Motion in One Dimension on Quantrex Academy →

More from Motion in One Dimension

A vehicle runs on a straight road of length 'L'. It travels half the distance with speed… MHT CET Medical 2026 For uniform acceleration in linear motion which of the following is NOT CORRECT ? MHT CET Medical 2026 Two cars, P and Q move toward each other, getting 8\ m closer every second. If they move… MHT CET Medical 2026 A block is kept on the floor of an elevator at rest. The elevator starts descending with… MHT CET Medical 2026 The acceleration (a ) -time (t ) graph for the body starting from rest is as shown in the… MHT CET Medical 2026 A train accelerates from rest at a constant rate 'p' for some time (attains velocity 'v')… MHT CET Medical 2026 The following plots show variation of velocity ( v ) with time ( t ), of a ball thrown… NEET 2026 Consider a particle moving along a straight line, whose position as a function of time is… NEET 2026 Full Motion in One Dimension list All NEET PYQs