Question

acceleration of a particle is given by a=t3-3t2+5 where t is time in sec and a is acceleration in m/s2 then what is the velocity when t =2​

Answer 1

Answer:

a = t³ - 3t² + 5

Now, a = dv/dt

So,

dv = (t³-3t²+5) dt

Now we're integrating this with the required limits i.e v=0 to v='v' and t=0 to t=2.

$\int\limits^v_0 {} \, dv = \int\limits^2_0 {t^3-3t^2+5} \, dt$

v - 0 = (2⁴-0⁴)/4 - 3*(2³-0³)/3 + 5*(2-0)

or v = 16/4 - 3*8/3 + 5*2 = 4 - 8 + 10 = 6

Therefore the required velocity is 6 m/s.