(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.

(a).  Three equations of uniformly accelerated motion are as below:

(i). $v=u+at$

(ii). $s=ut+\frac{1}{2}at^2$

(iii). $v^2=u^2+2as$

Here, $u\rightarrow$ initial velocity

$v\rightarrow$ final velocity

$a\rightarrow$ acceleration 

$t\rightarrow$ time

$s\rightarrow$ displacement

(b). Here initial velocity $u=0$

Final velocity $v=72\ km/h=72\times\frac{5}{18}=20\ m/s$

Time $t=10\ seconds$

Therefore:

(i).  Acceleration $a=\frac{change\ in\ velocity}{time}$

$=\frac{v-u}{t}$

$=\frac{20-0}{10}$

$=2\ m/s^2$

Therefore, acceleration is $2\ m/s^2$.

(ii).  as known, the average velocity $=\frac{u+v}{t}$

$=\frac{0+20}{10}$

$=2\ m/s$

Therefore, average velocity of the car $2\ m/s$.

(iii).  Let $s$ be the distance travelled by car.

On using the equation of motion $s=ut+\frac{1}{2}at^2$

$s=0+\frac{1}{2}\times2\times10^2$

Or $s=100\ m$

Therefore, distance travelled by the car is $100\ m$.

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Updated on: 10-Oct-2022

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