A particle moves rectilinearly with uniform acceleration. Its velocity at time t = 0 is V1 and at time t = t is V2. Average velocity of the particle in this time interval is V1+V22. Is this statement true or false? Substantiate your answer.

Acceleration of the particle: a=V2−V1tDisplacement of the particle: S=ut+12at2S=V1t+12V2−V1tt2⇒S=V1+V22tAverage velocity =St=V1+V22tt⟨V⟩=V1+V22Hence, the statements are true.

Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

A particle moves rectilinearly with uniform acceleration. Its velocity at time t = 0 is V₁ and at time t = t is V₂. Average velocity of the particle in this time interval is $\frac{V_{1} + V_{2}}{2}$ . Is this statement true or false? Substantiate your answer.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Acceleration of the particle: $a = \frac{V_{2} - V_{1}}{t}$
Displacement of the particle: $S = ut + \frac{1}{2} {at}^{2}$
$S = V_{1} t + \frac{1}{2} (\frac{V_{2} - V_{1}}{t}) t^{2} \Rightarrow S = (\frac{V_{1} + V_{2}}{2}) t$
Average velocity $= \frac{S}{t} = [\frac{V_{1} + V_{2}}{2 t}] t$
$⟨ V ⟩ = \frac{V_{1} + V_{2}}{2}$