(A) The velocity of an object is the time derivative of its position function,$V(t) = \frac{dR}{dt}$.For car $A$: $V_{A}(t) = \frac{d}{dt}(at + bt^2)

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(A) The velocity of an object is the time derivative of its position function,$V(t) = \frac{dR}{dt}$.For car $A$: $V_{A}(t) = \frac{d}{dt}(at + bt^2) = a + 2bt$.For car $B$: $V_{B}(t) = \frac{d}{dt}(xt - t^2) = x - 2t$.To find the time $t$ when the cars have the same velocity,we set $V_{A} = V_{B}$:$a + 2bt = x - 2t$Rearranging the terms to solve for $t$:$2bt + 2t = x - a$$t(2b + 2) = x - a$$t = \frac{x - a}{2(b + 1)}$.

Class 11 Physics Motion in Straight Line Instantaneous Velocity and Speed and Velocity-time Graph

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Two cars $A$ and $B$ start from a point at the same time in a straight line and their positions are represented by $R_{A}(t) = at + bt^2$ and $R_{B}(t) = xt - t^2$. At what time do the cars have the same velocity?

MHT CET 2023 All MHT CET

A
$\frac{x-a}{2(b+1)}$
B
$\frac{x+a}{2(b-1)}$
C
$\frac{x-a}{(b+1)}$
D
$\frac{x+a}{(b-1)}$

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Motion in Straight Line

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Instantaneous Velocity and Speed and Velocity-time Graph

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Two cars $A$ and $B$ start from a point at the same time in a straight line and their positions are represented by $R_{A}(t) = at + bt^2$ and $R_{B}(t) = xt - t^2$. At what time do the cars have the same velocity?

Similar Questions

The $x-t$ graph for a uniformly accelerated particle is as shown in the figure. Find the average velocity between points $(i)$ and $(ii)$ in $ms^{-1}$.

The position of a particle moving along the $x$-axis is given by $x = 10t - 2t^2$. Then the time $(t)$ at which it will momentarily come to rest is .......... $s$.

What is the acceleration of the particle on $OA$,$AB$,and $BC$ respectively?

The graph below shows the velocity versus time graph for a body. Which of the following graphs represents the corresponding acceleration $v/s$ time graph?

$A$ bird flies with a velocity $(t-2) \text{ m/s}$ along a straight line, where $t$ is the time in seconds. The distance covered by it in a time of $4 \text{ s}$ is: (in $\text{ m}$)

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