Question

29.
The initial velocity of a particle is u (at t = 0) and the
acceleration a is given by ft.
Which of the following relation is valid?
(a) v=u + ft2
(b) v=u+ft2/2
(c) v=u + ft
(d) v=u​

Answer 1

Correct Question :

The initial velocity of a particle is u (at t = 0) and the  acceleration a is given by ft.  Which of the following relation is valid ?

(a) v=u + ft²

(b) v=u+ft²/2

(c) v=u + ft

(d) v=u​

Solution :

Initial velocity of a particle (u) = u m/s

Acceleration (a) = ft m/s²

Final velocity (v) = v m/s

Time (t) = t s

⧪  Apply 1st equation of motion ,

➳ v = u + at

➳ v = u + (ft) t

➳ v = u + ft²  $\pink{\bigstar}$

Option (a)

More Info :

Equations of motion :

 v = u + at

 s = ut + ¹/₂ at²

 v² - u² = 2as

 Sₙ = u + ᵃ/₂ ( 2n - 1 )

Answer 2

Answer:

Option (a) Valid relation.

Explanation:

Given that,

• Initial velocity (u) = u m/s
• Final velocity (v) = v m/s
• Acceleration (a) = ft m/s²
• Time (t) = t sec

Applying acceleration formula,

$\green\bigstar$ ${\boxed{\red{\sf{ a = \frac{v - u}{t}}}}}$

[ Putting values ]

$\implies$ ft = (v - u)/t

$\implies$ (ft)t = v - u

$\implies$ ft² = v - u

$\implies$ v = u + ft² $\blue\bigstar$

Hence solved!!