Question

the displacement- time equation for an object is given below:
S= 2t3+5t+9

what will be the value of velocity at 2 sec?​

Answer 1

Answer:

$\boxed{\mathfrak{Velocity \ at \ 2 \ s = 29 \ m/s}}$

Explanation:

Displacement-time equation:

$\rm s = 2 {t}^{3} + 5t + 9$

Rate of change of displacement-time equation gives velocity:

$\rm \implies v = \dfrac{ds}{dt} \\ \\ \rm \implies v = \dfrac{d}{dt} (2 {t}^{3} + 5t + 9) \\ \\ \rm \implies v = 6 {t}^{2} + 5$

At t = 2 s:

$\rm \implies v = 6 \times {(2)}^{2} + 5 \\ \\ \rm \implies v = 6 \times 4 + 5 \\ \\ \rm \implies v = 24 + 5 \\ \\ \rm \implies v = 29 \: m {s}^{ - 1}$