Question

v=80m/s, u=20m/s,t=8s,a=7.5m/s2..so find the value of s ?? Give with proper SI unit​

Answer 1

Answer :

• s or distance is 400 m.

Given Information :

• Final velocity (v) = 80 m/s

• Initial velocity (u) = 20 m/s

• Time taken (t) = 8 s

• Acceleration (a) = 7.5 m/s²

To calculate :

• Distance (s)

Calculation :

Here, we can calculate distance in two ways,

• By using second equation of motion.
• By using third equation of motion.

$\underline{\small \sf {\maltese \; \; \; By \: using \: 2nd \: equation \: of \: motion : \; \; \; }}$

$\boxed { \rm {s = ut + \dfrac{1}{2}at^2 }}$

Substituting values,

$\hookrightarrow \rm { s = (20 \times 8) + \left ( \dfrac{1}{2} \times 7.5 \times (8)^2 \right ) }$

$\hookrightarrow \rm { s = 160 + \left ( \dfrac{1}{2} \times \dfrac{75}{10} \times 64 \right ) }$

$\hookrightarrow \rm { s = 160 + \left ( \dfrac{75}{10} \times 32 \right ) }$

$\hookrightarrow \rm { s = 160 +\left ( \dfrac{75}{5} \times 16 \right ) }$

$\hookrightarrow \rm { s = 160 + ( 15 \times 16) }$

$\hookrightarrow \rm { s = 160 + 240}$

$\hookrightarrow \boxed{\rm { s = 400 \: m} }$

$\underline{\small \sf {\maltese \; \; \; By \: using \: 3rd \: equation \: of \: motion : \; \; \; }}$

$\boxed { \rm {v^2 - u^2 = 2as }}$

$\hookrightarrow \rm { (80)^2 - (20)^2 = 2 \times 7.5 \times s}$

$\hookrightarrow \rm { 6400 -400= 2 \times \dfrac{75}{10} \times s}$

$\hookrightarrow \rm { 6000 = \dfrac{75}{5} \times s}$

$\hookrightarrow \rm { 6000 = 15 \times s}$

$\hookrightarrow \rm { \dfrac{6000 }{15}= s}$

$\hookrightarrow \boxed{\rm { s = 400 \: m} }$

Therefore, distance (s) is 400 m.

More Information :

First equation of motion :

• v = u + at

Second equation of motion :

• s = ut + ½at²

Third equation of motion :

• v² = u² + 2as

Where,

• v denotes final velocity

• u denotes initial velocity

• a denotes acceleration

• s denotes distance

• t denotes time