Question

a rock thrown down from a bridge has fallen 4t + 4.9t^2 meters.what is the velocity of the apple when t=3?​

Answer 1

Answer :

• The velocity of the rock on the position of 4t + 4.9t² at t = 3 s is 33.4 m/s.

Explanation :

Given :

• Displacement of the rock = 4t + 4.9t² m
• Instant of time, t = 3 s

To find :

• Velocity of the rock at the given instant of time, v = ?

Knowledge required :

• By differentiating the displacement of a particle , we will get the velocity of the particle.

Velocity of a particle is given the position of the particle with respect to t .i.e,

⠀⠀⠀⠀⠀=> v = d(s)/d(t)

• Exponent rule of differentiation :

If y = nx^n, then the derivative of the function w.r.t x will be :

⠀⠀⠀⠀= d(nx^n)/dx = n·x^(n - 1)

• According to the rule of exponent, if any number/digit has a exponent of zero, then it will be equal to 1. i.e, 2⁰ = 1.

Solution :

By differentiating the position of the rock with respect to t, we get :

⠀⠀⠀⠀=> d(s)/dt = d(4t + 4.9t²)/dt

⠀⠀⠀⠀=> d(s)/dt = d(4t¹)/dt + d(4.9t²)/dt

⠀⠀⠀⠀=> d(s)/dt = 1 × 4t¹ ⁻ ¹ + 2 × 4.9t² ⁻ ¹

⠀⠀⠀⠀=> d(s)/dt = 4t⁰ + 2 × 4.9t¹

⠀⠀⠀⠀=> d(s)/dt = 4 + 9.8t

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ v = d(4t + 4.9t²)/dx = 4 + 9.8t m/s

Hence the velocity of the rock is 4 + 4.9t m/s.

Now let us find the velocity of the rock at, t = 3 s :

By substituting the value of t in the velocity of the rock, we get :

⠀⠀⠀⠀=> v = 4 + 9.8t

⠀⠀⠀⠀=> v_(t = 3) = 4 + 9.8(3)

⠀⠀⠀⠀=> v_(t = 3) = 4 + 29.4

⠀⠀⠀⠀=> v_(t = 3) = 33.4

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ v_(t = 3) = 33.4 m/s

Therefore,

• Velocity of the rock at the given instant of time, v = 33.4 m/s

Answer 2

$\huge{\boxed{\rm{Question}}}$

A rock thrown down from a bridge has fallen 4t + 4.9t² meters . What is the velocity of the rock when t=3?

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• A rock thrown down from a bridge has fallen 4t + 4.9t² meters.

• Value of t = 3

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Velocity of the rock when t=3.

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that a rock is thrown down from a bridge has fallen 4t + 4.9t² meters. After that it ask us to find the velocity of a rock. Now, there is a hint that the value of t = 3.

$\large{\boxed{\boxed{\sf{How \: to \: solve \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• To solve this question firstly we have learn some concepts. These concept are written below for you. At last by understanding all the concept we get a rule that is d(nxⁿ) dx = n-xⁿ-¹. After that we have to put the values. At last we get a result that is v = 4 + 9.8 m/s. According to this result we have to put the values. But we have to remember that there is a hint given in the question that t = 3 . According to the given hint nd according to above result we have to substitute the values and at last we get our final result that is 33.4 m/s. And it's the velocity of rock.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• Velocity of the rock = 33.4 m/s

$\huge{\boxed{\rm{Compulsory \: to \: know}}}$

What is velocity and some others detail.

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time

In SI base units: m/s

Other units: mph, ft/s

Dimension: L T−1

How particle's velocity is given ?

Velocity of a particle is given the position of the with respect i.e.,

• v = d(s) / d(t)

What is exponential rule of differentiating ?

If y = = nxⁿ then the function derivatives of the function ᴡ.ʀ.ᴛ ᙭ will be the following -

d(nxⁿ) dx = n-xⁿ-¹

We know that there is one of the rule of exponent is that x⁰ = x¹ foe example 5⁰ = 5¹.

How we get velocity of any particle ?

Differentiating the particle's displacement we will get the velocity of the particle.

Now, respecting the values for the position of the rock respect to t we get the following results ✂

⇝ d(s) / dt = d( 4t + 4.9t² ) / dt

⇝ d(s) / dt = d ( 4t¹ ) / dt + d (4.9t² ) / dt

⇝ d(s) / dt = 1 / 4t¹ - ¹ + 2 × 4.9t²-¹

⇝ d(s) / dt = 4t⁰ + 2 × 4.9t¹

⇝ d(s) / dt = 4 + 9.8t

Therefore, v = d (4t + 4.t²) / dx

v = 4 + 9.8 m/s

Hence, the rock's velocity is 4 + 9.8 m/s.

Now, let's carry on,

According to the question now we have to find the velocity.

And a hint is given that the value of t is 3.

Now substituting the value we get,

↝ v = 4 + 9.8t

↝ v = 4 + 9.8 (3)

↝ v = 4 + 29.4

↝ v = 33.4

Hence, 33.4 m/s is the velocity of the rock.