At time $t=0$,a particle leaves the origin and moves in the positive direction of the $X$-axis. If the velocity of the particle varies as $v(t)=v_0(1-t/t_0)$,where $|v_0|=10 \ m/s$ and $t_0=10 \ s$,then the distance covered by the particle during the first $20 \ s$ is: (in $m$)

$A$ particle moving along a straight line covers the first half of the distance with a speed of $3 \, m \, s^{-1}$. The other half of the distance is covered in two equal time intervals with speeds of $4.5 \, m \, s^{-1}$ and $7.5 \, m \, s^{-1}$ respectively. The average speed of the particle during the motion is:

In what different ways can the velocity of an object be changed?

$A$ cyclist starts from the centre $O$ of a circular park of radius $1\; km$,reaches the edge $P$ of the park,then cycles along the circumference,and returns to the centre along $QO$ as shown in Figure. If the round trip takes $10 \;min$,what is the
$(a)$ net displacement,
$(b)$ average velocity,and
$(c)$ average speed of the cyclist?

$A$ 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 $g = 10 \text{ m/s}^2$)

For a particle showing motion under the force $F = -5(x - 2)^2$,the motion is .......