Kinematics of Motion in a Straight Line

Find the value of $V$.

Find the total time for which she is in motion from the instant that she passes $O$.

Show that $k = 3$ and $p = 26$.

Find the distance moved by the particle between the time at which its acceleration is zero and the time at which its velocity is zero.

Find the total time taken for the journey from $O$ to $P$.

On the given axes, sketch a displacement-time graph for the cyclist's journey from $O$ to $P$, showing on your graph the distances travelled after $10\text{ s}$ and $40\text{ s}$.

Find the time at which $X$ is instantaneously at rest, and hence find the total distance travelled by $X$ between $t = 0$ and $t = 16$.

A second particle $Y$ moves along another straight track, starting from a point $P$ at time $t = 0$. The acceleration of $Y$ at time $t\text{ s}$ is $a\text{ m s}^{-2}$, where $a = 0.8 - 0.6t$. The velocity of $Y$ when it leaves $P$ is $7.5\text{ m s}^{-1}$.

When the velocity of $Y$ is $-9.6\text{ m s}^{-1}$, show that the displacement of $X$ from $O$ is equal to the displacement of $Y$ from $P$.

On the given axes, sketch a velocity-time graph for the motion of the car between points $A$ and $B$.

The distance from $A$ to $B$ is $2750\text{m}$.

Find the value of $T$.

The car continues its journey from $B$, decelerating uniformly at $0.5\text{ms}^{-2}$ until it comes to rest at a point $C$ on the road.

Find the total distance from $A$ to $C$.

Find the maximum velocity of $P$ in the interval $0 \le t \le 3$.

It is given that in the interval $0 \le t \le 3$ the velocity of $P$ is always positive.

Find the distance of $P$ from $A$ at the instant when $P$ is moving at this maximum velocity.

Find the value of $T$.

Find the acceleration of the particle from $t = 50$ to $t = T$.

Find the velocity of $X$ at $t = 4$.

Find the value of $T$.

Find the total distance travelled by $X$ between $t = 0$ and $t = T$.

Find the values of $t$ when the velocity of $P$ is $100\text{ms}^{-1}$.

Show that there is a particular value of $t$ for which the velocity and acceleration of the particle are both zero.

Find the displacement of $P$ from $O$ at the time that the velocity and acceleration of the particle are both zero.