$A$ particle moves in a straight line such that its displacement $S$ (in $m$) at a time $t$ (in $sec$) is given by $S(t) = t^3 - 4t^2 + 7t$. The instantaneous velocity $v$ at $t = 4$ is (in $m/sec$)

$A$ particle moves along the curve $y=x^2+2x$. Then, the point on the curve such that the $x$ and $y$ coordinates of the particle change with the same rate is

If $f(x) = 2x^{2}$,find $\frac{f(3.8) - f(4)}{3.8 - 4}$.

$A$ particle is moving in a straight line according to the formula $s = t^2 + 8t + 12$. If $s$ is measured in meters and $t$ is measured in seconds,then the average velocity of the particle in the third second is .......... $m/s$.

If the law of motion in a straight line is $s = \frac{1}{2}vt$,then acceleration is

Consider a rectangle whose length is increasing at the uniform rate of $2 \, m/sec$,breadth is decreasing at the uniform rate of $3 \, m/sec$ and the area is decreasing at the uniform rate of $5 \, m^2/sec$. If after some time the breadth of the rectangle is $2 \, m$,then the length of the rectangle is ........ $m$.