JEE Main · 2024 · 01 Feb 2024 · Shift 1 · Kinematics

WhatsApp Email

A particle is moving in one dimension (along x axis) under the action of a variable force. It's initial position was 16 m right of origin. The variation of its position (x) with time (t) is given as

x = - 3 t^{3} + 18 t^{2} + 16 t

, where

x

is in m and

t

is in s. The velocity of the particle when its acceleration becomes zero is ______ m/s.

Answer: 52

Solution

Position:

x = - 3 t^{3} + 18 t^{2} + 16 t

. Velocity:

v = \frac{d x}{d t} = - 9 t^{2} + 36 t + 16

. Acceleration:

a = \frac{d v}{d t} = - 18 t + 36

.
Setting

a = 0

t = 2

v (2) = - 9 (4) + 36 (2) + 16 = - 36 + 72 + 16 = 52 m/s

JEE Main · 2024 · 01 Feb 2024 · Shift 1 · Integer answer

Practise more: all JEE Main PYQs on Kinematics →

More JEE Main questions on Kinematics

A projectile is thrown upward at an angle $6 0^{\circ}$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $4 5^{\circ}$ with the horizontal. The initial speed of the projectile is ______ m/s.
JEE Main 2026View solution →
A river of width 200 m is flowing from west to east with a speed of $18 km / h$ . A boat, moving with speed of $36 km / h$ in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for thi …
JEE Main 2026View solution →
An object is projected with kinetic energy K from a point A at an angle $6 0^{\circ}$ with the horizontal. The ratio of the difference in kinetic energies points B and C to that at point A (see figure), in the absence of air friction is :
JEE Main 2026View solution →
A block is sliding down on an inclined plane of slope $θ$ and at an instant $t = 0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$ . The distance $(S)$ travelled by the block before its velocity become zero, …
JEE Main 2026View solution →
A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with $3 m / s^{2}$ . At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is …
JEE Main 2026View solution →
A bead $P$ sliding on a frictionless semi-circular string $(A C B)$ and it is at point $S$ at $t = 0$ and at this instant the horizontal component of its velocity is $v$ . Another bead $Q$ of the same mass as $P$ is ejected from point $A$ at $t = 0$ …
JEE Main 2026View solution →