Question

6. The displacement of a body as a function of time is given by s = 3t²+4t+7. Calculate the
magnitude of its instantaneous velocity and acceleration at t= 1s​

Answer 1

Answer:

10m/s

Explanation:

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Answer 2

Given,

➞ Displacement of a body is given as a function of time , s = 3t² + 4t + 7

We need to find instantaneous velocity, at t = 1s

Now that we know,

v = ds/dt

So, Differentiate both sides of the equation w.r.t t

⇒ ds / dt = d(3t² + 4t + 7) / dt

⇒ v = 3dt² / dt + 4dt/dt + d7/dt

⇒ v = 6t + 4 + 0

⇒ v = 6t + 4

We needed to find instantaneous velocity at t = 1 s, So substitute t = 1

⇒ v = 6(1) + 4

⇒ v = 10 units/s

Hence, Instantaneous velocity at t = 1 s is 10 units/s.

Properties Used :-

◉ d(u + v) / dz = du/dz + dv/dz

◉ dxⁿ / dx = nxⁿ⁻¹

◉ d(a) = 0 , Where a is constant

Some Information :-

☛ Instantaneous velocity is ds/dt which means change in displacement per unit time, Since the time interval and change in displacement are too small hence, The ratio of ∆s / ∆t is called instantaneous velocity at a time t.

⇒ a = dv/dt

⇒ v = ds/dt = ∫adt

⇒ s = ∫vdt