b$)$ Distinguish between scalar and vector quantities and give one example of each.

$(3$ marks$)$

c$)$ The speed of sound $v$ in a gas might plausibly depend on the pressure $p,$ the density $$ and the volume $v$ of the gas. Use dimensional analysis to determine the exponents $x,y$ and z in the formula.

$v=C{p}^x{}^y{v}^z$

where C is a dimensionless constant.

d$)$ State the significance of Newton's third law of motion

$(6$ marks$)$

$(1$ mark$)$

e$)$ Distinguish between average velocity and instantaneous velocity and give their relationship

f$)$ Define the terms impulse and linear momentum

$(3$ marks$)$

$(2$ marks$)$

g$)$ A $10$ g metal bob attached to an inelastic string is whirled in a circular path of radius $15$ cm at an angular velocity of $5ra\frac{d}{sec}.$ Calculate the centripetal force experienced by the bob.

h$)$ A $1\mathrm{.}75$ kg particle moves as function of time as follows:

$(3$ marks$)$

$x=4cos(1\mathrm{.}33t+\frac{}{5})$

where distance is measured in metres and time in seconds.

Determine;

i$)$ the amplitude, frequency, angular frequency, and period of this motion

ii$)$ the equation of the velocity of this particle

$(3$ marks$)$

iii$)$ the equation of the acceleration of this particle

$(1$ mark$)$

$(1$ mark$)$

i$)$ A particle moving in space has its displacement described by the vector

vec$(r)=4t^3$hat$()+6t^2$hat$()+7$hat$(k)$

If the particle has travelled for $5$ seconds, determine

i$)$ Its velocity

ii$)$ Its acceleration

$(3$ marks$)$

$(2$ marks$)$