Two cars start from a point at the same time in a straight line and their positions are represented by $x_1(t) = at + bt^2$ and $x_2(t) = Ft - t^2$. At what time do the cars have the same velocity?

$A$ cyclist traversed half the distance of a linear track with a velocity $10 \ m \ s^{-1}$. The remaining part of the track was covered with a velocity $v_1$ for half the time and a velocity $v_2$ for the other half of the time. If $v_1+v_2=20 \ m \ s^{-1}$, then the average velocity of the cyclist during the completion of the journey through the track is (in $m \ s^{-1}$)

State whether the following statements are true or false:
$(a)$ If the motion is not along a straight line,then path length = magnitude of displacement.
$(b)$ Stopping distance is directly proportional to the initial velocity.
$(c)$ The average speed of an object moving with different speeds is the average of those speeds.
$(d)$ The area under the position-time graph represents the displacement of the moving object.

$A$ particle moves along the straight line $y=3x+5$. Which coordinate changes at a faster rate?

$A$ gas balloon is going up with a constant velocity of $10 \text{ m/s}$. When this balloon reached a height of $75 \text{ m}$, a stone is dropped from it and the balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is . . . . . . $\text{m}$. (Take $g = 10 \text{ m/s}^2$)

$A$ street car moves rectilinearly from station $A$ to the next station $B$ with an acceleration varying according to the law $a = (b - cx)$,where $b$ and $c$ are constants and $x$ is the distance from station $A$. The distance between the two stations and the maximum velocity are: