Question

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

Answer 1

(i) First equation of motion: $v=u+at$ (Where 'u' is the initial velocity, 'v' is the final velocity, 'a' is the acceleration and 't' is the time taken)

Second equation of motion: $s=ut+\frac{1}{2}a{t}^2$ (Where 's' is the displacement, 'u' is the initial velocity, 'a' is the acceleration and 't' is the time taken)

Third Equation of motion: $v^2=u^2+2as$ (Where 'u' is the initial velocity, 'v' is the final velocity, 'a' is the acceleration and 's' is the displacement)

(ii) (a) Initial velocity of the body = 0 m/s

Final velocity of the body = 72 km/h = $72\times \frac{1000\mathrm{m}}{3600\mathrm{s}}=20\mathrm{m}/\mathrm{s}$

Time taken = 10 s

Acceleration = $\frac{\mathrm{Final}\mathrm{velocity}-\mathrm{Initial}\mathrm{velocity}}{\mathrm{Time}\mathrm{taken}}=\frac{20\mathrm{m}/\mathrm{s}-0}{10\mathrm{s}}=2\mathrm{m}/{\mathrm{s}}^2$

Hence, the acceleration produced is 2 m/s²

(b) Using the second equation of motion, $s=ut+\frac{1}{2}a{t}^2$

$$\begin{gathered} \Rightarrow s=0+\frac{1}{2}\left(2\right)(10{)}^2=100\mathrm{m} \\ \Rightarrow \mathrm{s}=100\mathrm{m} \end{gathered}$$

Total displacement = 100 m

Average velocity = $\frac{\mathrm{Total}\mathrm{displacement}}{\mathrm{Total}\mathrm{time}\mathrm{taken}}=\frac{100\mathrm{m}}{10\mathrm{s}}=10\mathrm{m}/\mathrm{s}$

(c) Here, the body is traveling in a straight line motion. So, displacement is equal to the distance.

Hence, distance travelled by the body is the same as the displacement calculated above. i.e. 100 m.