Question:
A particle moves along a straight line such that its displacement at any time t is given by $s = (t^3-6t^2+3t+4)$ metres.
The velocity when the acceleration is zero is
A particle moves along a straight line such that its displacement at any time t is given by $s = (t^3-6t^2+3t+4)$ metres.
The velocity when the acceleration is zero is
Updated On: May 2, 2024
- 3 m/s
- 42 m/s
- -9 m/s
- -15 m/s
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Displacement (s) $t^3-6t^2+3t+4$ metres.
velocity (v) $=\frac{ds}{dt} = 3t^2 - 12t + 3 $
acceleration (a) $ =\frac{dv}{dt} = 6t - 12 $
When a = 0, we get t = 2 seconds.
Therefore velocity when the acceleration is zero
$(v) \, \, = 3 \times (2)^2 -(12 \times 2) + 3 = - 9\, m/s.$
velocity (v) $=\frac{ds}{dt} = 3t^2 - 12t + 3 $
acceleration (a) $ =\frac{dv}{dt} = 6t - 12 $
When a = 0, we get t = 2 seconds.
Therefore velocity when the acceleration is zero
$(v) \, \, = 3 \times (2)^2 -(12 \times 2) + 3 = - 9\, m/s.$
Was this answer helpful?
1
0
Top Questions on Motion in a straight line
- The displacement and the increase in the velocity of a moving particle in the time interval of \( t \) to \( (t + 1) \) s are 125 m and 50 m/s, respectively. The distance travelled by the particle in \( (t + 2)^{\text{th}} \) s is \( \_\_\_\_ \) m.
- JEE Main - 2024
- Physics
- Motion in a straight line
- A bus moving along a straight highway with speed of 72 km/h is brought to halt within 4s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is _______m.
- JEE Main - 2024
- Physics
- Motion in a straight line
- Pebbles are dropped freely for every half second into a river from a bridge above it. When the first pebble is about to strike the surface of the water, the fifth pebble is dropped. Then the height from the surface of the water from which the pebbles are dropped is (Acceleration due to gravity = 10 m/s²).
- TS EAMCET - 2024
- Physics
- Motion in a straight line
- A long straight wire carrying a current 3 A produces a magnetic field \( B \) at a certain distance. The current that flows through the same wire will produce a magnetic field \( \frac{B}{3} \) at the same distance is:
- KEAM - 2024
- Physics
- Motion in a straight line
- The motion of a cylinder on an inclined plane is:
- KEAM - 2024
- Physics
- Motion in a straight line
View More Questions
Questions Asked in NEET exam
- The E° value for the Mn3+/Mn2+ couple is more positive than that of Cr3+/Cr2+ or Fe3+/Fe2+ due to change of
- NEET (UG) - 2024
- Electronic configuration of atoms and ions
- The compound that will undergo SN1 reaction with the fastest rate is
- NEET (UG) - 2024
- Organic Chemistry- Some Basic Principles and Techniques
- Auxin is used by gardener to prepare weed-free lawns. But no damage is caused to grass as auxin
- NEET (UG) - 2024
- Role of auxin
- In an ecosystem if the Net Primary Productivity (NPP) of first trophic level is 100x (kcal m-2)yr-1, what would be the GPP (Gross Primary Productivity) of the third trophic level of the same ecosystem?
- NEET (UG) - 2024
- Ecosystems
- Arrange the following elements in increasing order of electronegativity:
N, O, F, C, Si
Choose the correct answer from the options given below:- NEET (UG) - 2024
- Modern Periodic Law And The Present Form Of The Periodic Table
View More Questions
Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.