Question

The position of a particle is given by x = 4 - 5t - t2, where x is in metre and t is in second. Find its instantaneous velocity at 2s.​

Answer 1

Answer:

-9m/s

Explanation:

V=dx/dt

Dx/dt=(-5)-2t

V=(-5)-2t

Putting t=2 seconds,

V=(-9)m/s

Answer 2

Answer :

• The velocity of the particle (at, t = 2 s) is (-9) m/s.

Explanation :

Given :

• Position of the particle, x = 4 - 5t - t² m.
• Instant of time, t = 2 s

To find :

• Instantaneous velocity of the particle, v = ?

Knowledge required :

• If we differentiate the position of the particle, we will get it's instantaneous velocity.

We know that the instantaneous velocity of a particle is its derivative of it's position with respect to time.

So,

⠀⠀⠀⠀⠀⠀⠀⠀⠀v = d(x)/dt⠀

[Where, v = Instantaneous Velocity of the particle, x = Position of the particle.]

• Rules of differentiation :

1. Differentiation of a constant term is 0., i.e, d(c)/dt = 0.
2. Exponent rule of differentiation, d(x^n)/dx = nx^(n - 1).

Solution :

By using the formula for Instantaneous velocity of a particle and substituting the values in it, we get :

⠀⠀=> v = d(x)/dt

⠀⠀=> v = d(x)/dt = d(4 - 5t - t²)/dt

⠀⠀=> v = d(x)/dt = d(4)/dt + d(-5t)/dt + d(-t²)/dt

⠀⠀=> v = d(x)/dt = 0 + (-5) + 2(-t)⁽² ⁻ ¹⁾

⠀⠀=> v = d(x)/dt = -5 - 2t

⠀⠀⠀⠀⠀⠀⠀⠀∴ v = -(5 + 2t) m/s

Hence the instantaneous velocity of the particle is -(5 + 2t) m/s.

Now let us find out the instantaneous velocity of the particle at , t = 2 s.

⠀⠀=> v = d(x)/dt = -(5 + 2t)

⠀⠀=> v₍ₜ ₌ ₂ ₛ₎ = -[5 + 2(2)]

⠀⠀=> v₍ₜ ₌ ₂ ₛ₎ = -(5 + 4)

⠀⠀=> v₍ₜ ₌ ₂ ₛ₎ = - 9

⠀⠀⠀⠀⠀⠀⠀⠀∴ v₍ₜ ₌ ₂ ₛ₎ = (-9) m/s

Hence, the instantaneous velocity of the particle at , t = 2 s, v = (-9) m/s.