Question

body moves from rest with uniform acceleration and travels 250 m in 5 s. Find the velocity of the body at 10 s after the start. ​

Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

• Displacement, (S) = 250 m
• Time taken, (t) = 5 sec.
• Initial velocity, (u) = 0

$\underline{\bf{Explanation\::}}$

As we know that 2nd equation of motion;

$\boxed{\bf{S=ut + \frac{1}{2} at^{2}}}$

A/q

→ 250 = 0 × 5 + 1/2 × a × (5)²

→ 250 = 0 + 1/2 × a × 25

→ 250 = 0 + 25a/2

→ 250 = 25a/2

→ 500 = 25a

→ a = 500/25

→ a = 20 m/sec²

Now,

We will using 1st equation of motion a/c to the given time;

Time, (t) = 10 sec.

$\boxed{\bf{v = u + at}}$

→ v = 0 + 20 × 10

→ v = 0 + 200

→ v = 200 m/sec.

Thus,

The final velocity of the body at 10 sec after start will be 200 m/sec.

Answer 2

Question:

A body moves from rest with uniform acceleration and travels 250 m in 5 s. Find the velocity of the body at 10 s after the start. 

Required To Find:

Velocity of the body

✪SOLUTION✪

Given,

Initial Velocity (u) = 0

Displacement (s) = 250m

Time Taken (t) = 5s

____________________________

Equation of motion for a body moving with constant acceleration along a straight line.

$✯\boxed {\red{\bf{V = u+at}}}$

$✯\boxed {\sf{s = (\frac{u+v}{2})t}}$

$✯\boxed {\red{\bf{s = ut+\frac{1}{2}at²}}}$

$✯\boxed {\sf{v² = u²+2as}}$

$✯\boxed {\sf{Sn = u+a(n-\frac{1}{2}}}$

____________________________

$\green {\sf{s = ut+\frac{1}{2}at²}}$

$➝\;{250 = 0×5+\frac{1}{2}×a×5²}$

$➝\; {250×2 = a × 25}$

$➝\;{a = \frac {250×2}{25}}$

$➝\;{a = 20 m/s²}$

Now by putting the value of a in

$\green{\sf{V = u+at}}$

Here time will be 10 sec

$→ {V = 0+20×10}$

$→ {V = 200}$

$\pink{\underline{\underline{\bf{Required\;AnSweR:}}}}$

☞ Velocity = $\fbox\purple {200m/s}$