Question

(a) Write the three equations of uniformly accelerated motion. Give the meaning of each symbol which occurs in them.
(b) A car acquires a velocity of 72 km per hour in 10 seconds starting from rest. Find (i) the acceleration, (ii) the average velocity, and (iii) the distance travelled in this time.

Answer 1

(a) The first equation of motion is-
$\boxed{v=u+at}$
Second equation of motion is-
$\boxed{s=ut+\frac{1}{2}a{t}^2}$
Third equation of motion is-
$\boxed{v^2=u^2+2as}$
Where,
(s) - Displacement
(u) - Initial velocity
(a) - Acceleration
(v) - Final velocity
(t) - Time taken

(b) We have the following information,
Initial velocity, (u) = 0 m/s
Final velocity
$$\begin{gathered} \left(v\right)=72\mathrm{km}/\mathrm{hr} \\ =\frac{72\left(1000\right)}{3600}\mathrm{m}/\mathrm{s} \\ =20\mathrm{m}/\mathrm{s} \\ \mathrm{Time}\mathrm{taken},\left(t\right)=\left(10\right)\mathrm{s} \end{gathered}$$

(i) So acceleration,
$a=\frac{v-u}{t}$
Put the values in the above equation to get the value of acceleration
$$\begin{gathered} a=\frac{20-0}{10} \\ =\boxed{2\mathrm{m}/{\mathrm{s}}^2} \end{gathered}$$

(ii) We have to find the average velocity. We will use the following relation,

$$\begin{gathered} \mathrm{Average}\mathrm{velocity}=\frac{\mathrm{Initial}\mathrm{velocity}+\mathrm{Final}\mathrm{velocity}}{2} \\ \mathrm{So},\mathrm{Average}\mathrm{velocity}=\frac{\mathit{v}\mathit{+}\mathit{u}}{\mathit{2}} \end{gathered}$$ Therefore putting the value in the above to get the average velocity,

$$\begin{gathered} \mathrm{Average}\mathrm{velocity}=\frac{20+0}{2}\mathrm{m}/\mathrm{s} \\ =\boxed{10\mathrm{m}/\mathrm{s}} \end{gathered}$$

(iii) We have to calculate the distance travelled. We will use the relation,
Distance travelled = (Average velocity) (Time)
So distance travelled is,
$$\begin{gathered} =\left(10\right)\left(10\right)\mathrm{m} \\ =\boxed{100\mathrm{m}} \end{gathered}$$