Question

If the velocity of a particle is (10 + 2t2) m/s, then
the average acceleration of the particle between
2s and 5s is
(1) 2 m/s2
(2) 4 m/s2
(3) 12 m/s2
(4) 14 m/s2​

Answer 1

Answer:

Given:

Velocity function of a particle has been provided as follows

v = 10 + 2t²

To find:

Average acceleration of the particle.

Concept:

Average acceleration is the ratio of the change in velocity and the change in time.

Note that it's different from instantaneous velocity.

acceleration avg. = ∆v/∆t

Calculation:

Velocity at t = 2 seconds :

v1 = 10 + (2 × 2²) = 1

=> v1 = 18 m/s

Velocity at t = 5 seconds :

v2 = 10 + (2 × 5²)

=> v2 = 60 m/s

Now net time taken = 5 - 2 = 3 seconds.

∴ Avg. acc = ∆v/∆t

=> Avg. acc = (60 - 18)/3

=> Avg. acc. = 14 m/s²

So average acceleration is 14 m/s²

Answer 2

Answer:

$\huge{\boxed{\mathfrak\green{Answer\::4)14m/{s}^{2}}}}$

Given that,

Velocity of the particle = (10 + 2t^2) m/s

To find,

Average acceleration of the particle between 2s and 5s .

Solution:-

Average acceleration =Net velocity/Net time.

Firstly at time = 2s

$\tt V = (10 + 2\times {2}^{2}) \\ \\ \Rightarrow\tt V = (10 + 2 \times 4) m/s \\ \\ \Rightarrow\tt V = 18 \: m/s$

Secondly at time = 5s

$\tt V =(10 + 2\times {5}^{2}) m/s \\ \\ \Rightarrow\tt V = (10 + 2\times 25) m/s \\ \\ \Rightarrow\tt V = 60 \: m/s$

_________________________

$\tt Net\: velocity = <strong>(</strong><strong> </strong><strong>6</strong><strong>0</strong><strong> </strong><strong>-</strong><strong> </strong><strong>1</strong><strong>8</strong><strong>)</strong><strong> </strong><strong>m</strong><strong>/</strong><strong>s</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong>\Rightarrow\tt Net \:velocity = 42\:m/s$

__________________________

$\tt Net\: time = <strong>(</strong><strong>5</strong><strong> </strong><strong>-</strong><strong> </strong><strong>2</strong><strong>)</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>s</strong><strong> </strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>R</strong><strong>i</strong><strong>g</strong><strong>h</strong><strong>t</strong><strong>a</strong><strong>r</strong><strong>r</strong><strong>o</strong><strong>w</strong><strong>\</strong><strong>t</strong><strong>t</strong><strong> </strong><strong>Net</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>t</strong><strong>i</strong><strong>m</strong><strong>e</strong><strong> </strong><strong>=</strong><strong> </strong><strong>3</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>s</strong><strong> </strong>\\ \\ \therefore\tt Average\: acceleration =\frac{42\:m/s }{3\:s} \\ \\ \Rightarrow\tt Average \:accelaration = 14 m/{s}^{2}$