A particle moves along X-axis as x = 4(t - 2) | vedclass

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

Question

(B) Given the position equation: $x = 4(t - 2) + a(t - 2)^2$.To find the velocity,we differentiate $x$ with respect to time $t$:$v = \frac{dx}{dt} = \

Vedclass · Accepted Answer

The acceleration of the particle is $2a$.

Vedclass · Answer

(B) Given the position equation: $x = 4(t - 2) + a(t - 2)^2$.To find the velocity,we differentiate $x$ with respect to time $t$:$v = \frac{dx}{dt} = \frac{d}{dt}[4(t - 2) + a(t - 2)^2] = 4 + 2a(t - 2)$.To find the acceleration,we differentiate the velocity with respect to time $t$:$a_{acc} = \frac{dv}{dt} = \frac{d}{dt}[4 + 2a(t - 2)] = 2a$.Checking the options:$(a)$ Initial velocity at $t = 0$ is $v = 4 + 2a(0 - 2) = 4 - 4a$,which is not $4$ unless $a = 0$.$(b)$ The acceleration is $2a$,which is constant and matches the derived result.$(c)$ At $t = 0$,$x = 4(0 - 2) + a(0 - 2)^2 = -8 + 4a$,which is not $0$ unless $a = 2$.Therefore,option $(b)$ is correct.

$A$ particle moves along $X-$axis as $x = 4(t - 2) + a(t - 2)^2$. Which of the following is true?

Similar Questions

The distance $x$ covered in time $t$ by a body having initial velocity $u$ and having constant acceleration $a$ is given by $x=ut+\frac{1}{2}at^2$. This result follows from

If the velocity of a particle is $v = At + Bt^2$,where $A$ and $B$ are constants,then the distance travelled by it between $1 \ s$ and $2 \ s$ is

$A$ $150 \,m$ long train is moving with a uniform velocity of $45 \,km/h$. The time taken by the train to cross a bridge of length $850 \,m$ is..........$sec$.

$A$ body starts from rest with uniform acceleration. If its velocity after $n$ seconds is $\upsilon$,then its displacement in the last two seconds is

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement $(s)-$ velocity $(v)$ graph of this object is

Vedclass Test Series

Exam Paper Generator

Online Exam Module