Question

6.The displacement of a particle is given by x(t)=4t2 +8t meter. Its velocity at t = 5 second is
(a) 16 m/s
(b) 32m/s
(c) 48m/s
(d) 64m/s

Answer 1

Displacement of the particle , x(t) = 4t² + 8t m

We need to find velocity at t = 5 s

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Velocity : It is defined as displacement covered per unit time

Instantaneous Velocity : It is defined as the velocity of a particle at particular instant of time .

$\longrightarrow \sf v=\Delta t\to 0\ \dfrac{\Delta x}{\Delta t}$

$\sf \longrightarrow v=\dfrac{dx}{dt}$

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$:\implies \sf x=4t^2+8t$

Velocity is given by ,

$:\implies \sf v=\dfrac{dx}{dt}$

$:\implies \sf v=\dfrac{d}{dt}\big(4t^2+8t\big)$

$:\implies \sf v=4(2t)+8(1)$

$:\implies \sf v=8t+8$

Velocity at t = 5 s is called as Instantaneous velocity and is given by ,

$:\implies \sf v=8(5)+5$

$:\implies \sf v=40+8$

$:\implies \sf v=48\ m/s\ \; \pink{\bigstar}$

Option (c)

Answer 2

Explanation:

x = 4t² +5

(1) v = dx/dt = 1+5

at t =2s , v = 1 × 2 +5 =7

(2) Average , velocity = displacement / time

at t =2 , x = 4 (2)² + 5 × 2 = 26 m

t = 3 , x = 4 (3)² + 5 × 3 = 64 m

average velocity = 64- 26/ 3-2

= 20 m/s

in your option all are wrong this answer is correct one .