Question

Find the distance travelled of the body before coming to rest of the body travel with the speed of 25 km per second and stopped in 25 seconds

Answer 1

Given :-

Initial velocity of body(u).= 25km/s

25km/s = 25000m/s

Final velocity of car(v) = 0

Time (t)= 25 seconds !

To find :-

Distance covered by body in the given time !

• First find acceleration

$\boxed{\sf{\dag\ \ v= u+at}}$

$\longrightarrow\sf 0= 25000+a\times 25\\ \\ \longrightarrow\sf -25000= 25a\\ \\ \longrightarrow\sf \cancel{\dfrac{-25000}{25}}= a\\ \\ \longrightarrow\sf -1000m/s^2= a$

$\boxed{\sf{\dag\ \ Acceleration\ produced \ by\ body= -1000m/s^2}}$

• Now find the distance

$\boxed{\sf{\bigstar{\ \ \ v^2=u^2+2as}}}$

$\longrightarrow\sf [0]^2= (-25000)^2 + 2\times -1000\times s\\ \\ \longrightarrow \sf 0= 625000000 -2000\times s\\ \\ \longrightarrow\sf -625000000 = -2000 \times s\\ \\ \longrightarrow\sf \dfrac{-625000\cancel{000}}{-2\cancel{000}}= s\\ \\ \longrightarrow\sf \cancel{\dfrac{-625000}{-2}}= s\\ \\ \longrightarrow\sf 312500m= s\\ \\ \bullet\sf \ \ Convert \ Into\ \ km\ \ \\ \\ \longrightarrow\sf s= 312.5km$

$\boxed{\textsf{ Distance \ covered \ by \ body = {\textbf{312.5km}}}}$

Answer 2

Distance travelled by body = 312,500 m or 312.5 km.

Solution

Initial speed of body = 25 km/s

= (25 × 1000)m/s

= 25000 m/s

As it comes to rest, so final speed = 0

Time taken to come to rest = 25 seconds.

☢ Using 1st equation of motion :

◕ v = u + at

⇒ 0 = 25000 + a × 25

⇒ 25a = -25000

⇒ a = -25000/25

⇒ a = -1000 m/s²

[Note : Negative sign shows retardation ]

∴ Acceleration of body = -1000 m/s²

Now using 2nd equation of motion :

◕ s = ut + ½ at²

⇒ s = (25000 × 25) + ½ × (-1000) × 25²

⇒ s = 625000 - 500 × 625

⇒ s = 625000 - 312500

⇒ s = 312,500 m or,

⇒ s = 312.5 km

∴ Distance travelled by body before coming to rest = 312,500 m or 312.5 km.