Jan Dangerfield, Stuart Haring and, Julian Gilbey Solutions for Exercise 5: EXERCISE 6B

A boy runs in a straight line. The velocity of the boy, $v{ \mathrm{ms}}^{-1}$, at time $t \mathrm{s}$ is given by:
$v=\left\{\begin{array}{c}2+3t:0⩽t⩽1\\ 6-t^2:1⩽t⩽1.2\\ 5-\frac{k}{30}t:1.2⩽t⩽T\end{array}\right.$ for $0⩽t⩽T$
The boy has velocity $0 \mathrm{m}{ \mathrm{s}}^{-1}$ at time $T$. Work out the average acceleration of the boy over the period $0-T$. Given that $k=11 \mathrm{and} \mathrm{T}=13.6 \mathrm{s}$.

A boy runs in a straight line. The velocity of the boy, $v{ \mathrm{ms}}^{-1}$, at time $t \mathrm{s}$ is given by:
$v=\left\{\begin{array}{c}2+3t:0⩽t⩽1\\ 6-t^2:1⩽t⩽1.2\\ 5-\frac{k}{30}t:1.2⩽t⩽T\end{array}\right.$ for $0⩽t⩽T$
The boy has velocity $0 \mathrm{m}{ \mathrm{s}}^{-1}$ at time $T$. The value for average acceleration is $13.6 \mathrm{m} {\mathrm{s}}^{-2}$ and $k=11$. Show that there is no time at which the acceleration of the boy is the same as his average acceleration. 

The motion of a cat, moving along a straight line, is modelled as $s=6t-t^2$ for small values of $t,$ where $s$ is measured in metres and $t$ in seconds.
Find an expression for the velocity of the cat as a function of time.

The motion of a cat, moving along a straight line, is modelled as $s=6t-t^2$ for small values of $t,$ where $s$ is measured in metres and $t$ in seconds.
Describe the motion of the cat.

The motion of a cat, moving along a straight line, is modelled as $s=6t-t^2$ for small values of $t,$ where $s$ is measured in metres and $t$ in seconds.
When does the cat come to momentary rest?

The motion of a cat, moving along a straight line, is modelled as $s=6t-t^2$ for small values of $t,$ where $s$ is measured in metres and $t$ in seconds.
Find the acceleration of the cat.

A particle moves forwards and backwards along a straight line. The velocity of the particle, $v \mathrm{m}{ \mathrm{s}}^{-1}$, at time $t$ s is given by $v=-t^3+75t$ for $0<t<10$. Find the maximum speed of the particle.

A robot moves along a straight line for $3 \mathrm{s}$. The displacement of the robot, $s \mathrm{m}$, from its initial position is given by $s=A{t}^3+B{t}^2+Ct$ for constants $A, B$ and $C,$ where $t$ is measured in seconds and $0<t<3$. The robot starts with velocity $2 \mathrm{m}{ \mathrm{s}}^{-1}$. It travels $6 \mathrm{m}$ before coming to rest at time $t=3 .$ Work out the values of $A, B$ and $C.$