Calculus for Kinematics (Edexcel IGCSE Further Pure Maths): Exam Questions

A particle $P$ is moving along the $x$-axis.

At time $t$ seconds $\left(t⩾0\right)$ the acceleration, $a$ m/s² , of $P$is given by $a=3t-4$

When$t=0$, $P$ is at rest.

Find the velocity of $P$ when $t=4$

At time $T$seconds, $T>0$, $P$ is instantaneously at rest.

Find the value of $T$

When $t=0$, $P$ is at the point with coordinates $\left(-10,0\right)$

Find the displacement of $P$ from the origin when $t=3$

A particle $P$ is moving along a straight line.

At time $t$ seconds $\left(t⩾0\right)$, the velocity, $v$ m/s, of $P$ is given by

$v=3t^2-16t+5$

Find the values of $t$ when $P$ is instantaneously at rest.

At time $t$ seconds the acceleration of $P$ is $a$ m/s²

Find the range of values of $t$ for which $a>0$

Find the distance, in m, that $P$ travels in the interval $1⩽t⩽4$

A particle $P$ is moving along the $x$-axis. At time $t$ seconds, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics»«mrow»«mi»t«/mi»«mo»§#10878;«/mo»«mn»0«/mn»«/mrow»«annotation encoding=¨application/vnd.wiris.mtweb-params+json¨»{¨fontFamily¨:¨Times New Roman¨,¨fontSize¨:¨18¨,¨autoformat¨:true,¨toolbar¨:¨«toolbar ref=`general`»«tab ref=`general`»«removeItem ref=`setColor`/»«removeItem ref=`bold`/»«removeItem ref=`italic`/»«removeItem ref=`autoItalic`/»«removeItem ref=`setUnicode`/»«removeItem ref=`mtext` /»«removeItem ref=`rtl`/»«removeItem ref=`forceLigature`/»«removeItem ref=`setFontFamily` /»«removeItem ref=`setFontSize`/»«/tab»«/toolbar»¨}«/annotation»«/semantics»«/math» , the velocity, $v\mathrm{m}/\mathrm{s}$, of $P$ is given by $v=2t^2-16t+30$

Find the acceleration, in $\mathrm{m}/{\mathrm{s}}^2$ , of $P$ when $t=5$

A particle $P$ is moving along the $x$-axis. At time $t$ seconds, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics»«mrow»«mi»t«/mi»«mo»§#10878;«/mo»«mn»0«/mn»«/mrow»«annotation encoding=¨application/vnd.wiris.mtweb-params+json¨»{¨fontFamily¨:¨Times New Roman¨,¨fontSize¨:¨18¨,¨autoformat¨:true,¨toolbar¨:¨«toolbar ref=`general`»«tab ref=`general`»«removeItem ref=`setColor`/»«removeItem ref=`bold`/»«removeItem ref=`italic`/»«removeItem ref=`autoItalic`/»«removeItem ref=`setUnicode`/»«removeItem ref=`mtext` /»«removeItem ref=`rtl`/»«removeItem ref=`forceLigature`/»«removeItem ref=`setFontFamily` /»«removeItem ref=`setFontSize`/»«/tab»«/toolbar»¨}«/annotation»«/semantics»«/math» , the velocity, $v\mathrm{m}/\mathrm{s}$, of $P$ is given by $v=2t^2-16t+30$

$P$ comes to instantaneous rest at the points $M$ and $N$ at times $t_1$ seconds and $t_2$ seconds where $t_2>t_1$

Find the exact distance $MN$

A particle $P$ moves along the $x$-axis.

At time $t$ seconds $\left(t⩾0\right)$ the acceleration, $a\mathrm{m}/{\mathrm{s}}^2$ , of $P$ is given by $a=6t-16$

When $t=0$, $P$ is at the origin and is moving with velocity 12 $\mathrm{m}/\mathrm{s}$.

Find an expression in terms of $t$ for

(i) the velocity of $P$ at time $t$ seconds

(ii) the displacement of $P$ at time $t$ seconds.

A particle $P$ moves along the $x$-axis.

At time $t$ seconds $\left(t⩾0\right)$ the acceleration, $a\mathrm{m}/{\mathrm{s}}^2$ , of $P$ is given by $a=6t-16$

When $t=0$, $P$ is at the origin and is moving with velocity 12 $\mathrm{m}/\mathrm{s}$.

Hence find the time at which $P$ first returns to the origin.