Question

A Particle moving with uniform
acceleration has gained a velocity of 15
m/s after 5 s and travels 18 m in its 7th
second of travel. The displacement of the
particle in the first three seconds of its
travel is​

Answer 1

Answer:

The displacement in first 3 seconds of travel is = 24 m.

Explanation:

Explained in the picture .

Answer 2

Given:

A Particle moving with uniform acceleration has gained a velocity of 15 m/s after 5 s and travels 18 m in its 7th second of travel.

To find:

Displacement in the first 3 seconds.

Calculation:

Let acceleration be a and initial velocity be u.

$\therefore \: v = u + at$

$= > \: 15 = u + (a \times 5)$

$= > \: 15 = u + 5a \: \: \: \: .......(1)$

Again, applying Equation of Kinematics:

$\therefore \: s = u + \dfrac{1}{2} a(2n - 1)$

$= > \: 18 = u + \dfrac{1}{2} a(2 \times 7 - 1)$

$= > \: 18 = u + \dfrac{1}{2} a(14- 1)$

$= > \: 18 = u + \dfrac{1}{2} a(13)$

$= > 36 = 2u + 13a \: \: \: \: \: ......(2)$

Solving eq.(1) and eq.(2) ;

$1) \: a = 2 \: m {s}^{ - 2}$

$2) \: u = 5 \: m {s}^{ - 1}$

Now, applying 2nd Equation of Kinematics:

$s = ut + \dfrac{1}{2} a {t}^{2}$

$= > s = (5 \times 3) +( \dfrac{1}{2} \times 2 \times {3}^{2} )$

$= > s = (15) +( \dfrac{1}{2} \times 2 \times 9)$

$= > s = 15 + 9$

$= > s = 24 \: m$

So, final answer is :

Displacement in first 3 seconds is 24 m.