Question

r=5t³–4t²+3t . Calculate the speed at 2s
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Answer 1

✪ Given info ✪

r=5t³–4t²+3t

• Here, r is the displacement
• t is the time

✪ Pre-requisite knowledge ✪

On differentiating distance with respect to time, we get velocity.

Differentiation of t³ is 3t²

Differentiaiton of t² is 2t.

Differentiation of 3t is 3.

✪ Process ✪

Let us assume speed be v

So, on differentiating r with respect to t(  $\frac{dr}{dt}$ ), we get :

r=5t³–4t²+3t

$\frac{dr}{dt}$ = 5(3t²) - 4(2t) + 3

v = 15t² - 8t + 3

For calculating speed at time 2 s, substitute t = 2.

v = 15(2)² - 8(2) + 3

v = 15(4) - 16 + 3

$\boxed{v = 47 m/s}$