Question

The velocity of a particle is given by v=2t²-3t+10 m/s. Find the instantaneous acceleration at t=5s.
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Answer 1

Given :

Velocity of the particle is given by v = 2t² - 3t + 10

To Find :

Instantaneous acceleration at t = 5 s

Concept :

The acceleration of a particle at a particular instant of time is called it's instantaneous acceleration

It is also defined as the limit of average acceleration as the time interval (∆t) become infinitesimally small .

If the time interval ∆t is chosen to be very small, i.e., as ∆t → 0, the corresponding accerlation is called instantaneous acceleration.

${\boxed{\bf{Instantaneous \: \: acceleration = \dfrac{\Delta V}{\Delta T} = \dfrac{dV}{dT}}}}$

Solution :

here, we should differentiate velocity

${\bf{v = 2t^2 - 3t + 10}}$

${\leadsto {\bf {a=\dfrac{dv}{dt}}}}\\\\{\leadsto{\bf {a=\dfrac{d}{dt}(2t^2-3t+10)}}}\\\\{\leadsto {\bf {a=4t-3}}}$

as per the question we have to find instantaneous accerlation in 5sec.

${\leadsto {\bf {a=4(5)-3}}}\\\\{\leadsto{\bf{a=20-3}}}\\\\{\leadsto{ \boxed {\bf {a=17\ m/s^2}}}}$

thus,the instantaneous acceleration at 5 sec is 17m/s².

$\:$

#sanvi....

Answer 2

Answer:

• Instantaneous acceleration of the particle at t = 5s is 17 m/s².

Explanation:

Given

• Velocity of particle with respect to t is given by, v = 2t² - 3t + 10 m/s

To find

• Instantaneous acceleration of the particle at 't = 5 s', a =?

Formula required

• Instantaneous acceleration 'a' is given by the differential coefficient of velocity 'v' with respect to time 't'.

        a = d(v) / d(t)

Solution

Using formula to find instantaneous acceleration

→ a = d(v) / d(t)

→ a = d( 2t² - 3t + 10 ) / d(t)

→ a = 4 t - 3 + 0

→ a = 4 t - 3

We need to find the 'a' at 't = 5 s', so

→ a(t) = 4t - 3

→ a(5) = 4 · 5 - 3

→ a(5) = 20 - 3

→ a(5) = 17 m/s²

Therefore,

• Instantaneous acceleration of the particle at 't = 5s' will be 17 m/s².