Question

A body starts from rest and accelerates uniformly at a rate of 5m/s2. calculate its velocity after 90m

Answer 1

it's certainly a bit untidy but I hope it helps.

Answer 2

Given that,

Initial velocity (u) = 0 m/s

Uniform acceleration = 5 m/s²

Distance = 90 m

To find,

Final velocity after 90 m = ?

As we know,

There are three equations of motions. They are as follows : -

(i) v = u + at

(ii) s = ut + $\frac{1}{2}$ at²

(iii) 2as = v² - u²

But here, we've to use the third equation of motion. We can't use rest of the equations because : -

[In (i)] Time and final velocity both are unknown. So, we can't calculate the Final velocity as there two unknown quantities.

[In (ii)] Here, in this equation, the Final velocity is absent. So, we can't calculate it.

So, we'll use third equation of motion to find the value of final velocity as all the values are given except the final velocity which we have to reckon.

By using third equation of motion,

2as = v² - u²

2(5)(90) = v² - (0)²

(10)(90) = v² - 0

900 = v²

- v² = - 900

$\cancel{-} v^2 = \cancel{-} 900$

v = $\sqrt{900}$

v = 30 m/s

Therefore, the body moves with the final velocity of 30 m/s after 90 m.

$\huge{\pink{\boxed{v = 30\:m/s}}}$