(B) The velocity is given by $v = \frac{dx}{dt} = v_{0} + gt + Ft^{2}$.To find the displacement $s$ at $t = 1$,we integrate the velocity with respect

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

$v_{0} + \frac{g}{2} + \frac{F}{3}$

(B) The velocity is given by $v = \frac{dx}{dt} = v_{0} + gt + Ft^{2}$.To find the displacement $s$ at $t = 1$,we integrate the velocity with respect to time from $t = 0$ to $t = 1$:$s = \int_{0}^{1} v dt = \int_{0}^{1} (v_{0} + gt + Ft^{2}) dt$$s = [v_{0}t + \frac{gt^{2}}{2} + \frac{Ft^{3}}{3}]_{0}^{1}$Substituting the limits $t = 0$ and $t = 1$:$s = (v_{0}(1) + \frac{g(1)^{2}}{2} + \frac{F(1)^{3}}{3}) - (0)$$s = v_{0} + \frac{g}{2} + \frac{F}{3}$

Class 11 Physics Motion in Straight Line Uniformly Accelerated Motion

Easy

The velocity of a particle is $v = v_{0} + gt + Ft^{2}$. Its position is $x = 0$ at $t = 0$; then its displacement after time $t = 1$ is:

JEE MAIN 2021 All JEE MAIN

A
$v_{0} + g + F$
B
$v_{0} + \frac{g}{2} + \frac{F}{3}$
C
$v_{0} + \frac{g}{2} + F$
D
$v_{0} + 2g + 3F$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Motion in Straight Line

Subtopic

Uniformly Accelerated Motion

Previous Year

JEE MAIN 2021 Paper All JEE MAIN years →

$A$ particle moves along a straight line in such a way that its acceleration is increasing at the rate of $2 m/s^3$. Its initial acceleration and velocity were $0$. The distance covered by it in $t = 3 s$ is ........ $m$.

View Solution

$A$ body starts moving from rest with constant acceleration. It covers a displacement $S_1$ in the first $(p-1)$ seconds and $S_2$ in the first $p$ seconds. The total displacement $S_1+S_2$ will be covered in time:

DifficultJEE MAIN 2024

View Solution

For a vehicle moving at $80 \, km/hr$, how many times is the stopping distance compared to a vehicle moving at $40 \, km/hr$, assuming both have the same deceleration (in $\times$)?

Medium

View Solution

Give an example of a motion where $x > 0$,$v < 0$,and $a > 0$ at a particular instant.

Difficult

View Solution

$A$ point moves with uniform acceleration and $v_1, v_2$ and $v_3$ denote the average velocities in the three successive intervals of time $t_1, t_2$ and $t_3$. Which of the following relations is correct?

Difficult

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The velocity of a particle is $v = v_{0} + gt + Ft^{2}$. Its position is $x = 0$ at $t = 0$; then its displacement after time $t = 1$ is:

Similar Questions

$A$ particle moves along a straight line in such a way that its acceleration is increasing at the rate of $2 m/s^3$. Its initial acceleration and velocity were $0$. The distance covered by it in $t = 3 s$ is ........ $m$.

$A$ body starts moving from rest with constant acceleration. It covers a displacement $S_1$ in the first $(p-1)$ seconds and $S_2$ in the first $p$ seconds. The total displacement $S_1+S_2$ will be covered in time:

For a vehicle moving at $80 \, km/hr$, how many times is the stopping distance compared to a vehicle moving at $40 \, km/hr$, assuming both have the same deceleration (in $\times$)?

Give an example of a motion where $x > 0$,$v < 0$,and $a > 0$ at a particular instant.

$A$ point moves with uniform acceleration and $v_1, v_2$ and $v_3$ denote the average velocities in the three successive intervals of time $t_1, t_2$ and $t_3$. Which of the following relations is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module