The acceleration of a particle in ms-2 is given by a = 3t2 + 2t + 2, w

1.	The acceleration of a particle in ms-2 is given by a = 3t2 + 2t + 2, where time t is in second. If the particle starts with a velocity v = 2 ms-1 at t = 0, then find the velocity at the end of 2 s.
Answer» As, a = 3t² + 2t + 2 ⇒ \(\frac{dv}{dt}\) = 3t² + 2t + 2 Integrating ∫ dv = ∫ (3t² + 2t + 2)dt v = t³ + t² + 2t + c at, t = 0, v = 0 ∴ c = 2 now at t=2, v= 8 + 4 + 4 + 2 = 18 m/s

The acceleration of a particle in ms-2 is given by a = 3t2 + 2t + 2, where time t is in second. If the particle starts with a velocity v = 2 ms-1 at t = 0, then find the velocity at the end of 2 s.

Answer»

As, a = 3t² + 2t + 2 ⇒ \(\frac{dv}{dt}\) = 3t² + 2t + 2

Integrating

∫ dv = ∫ (3t² + 2t + 2)dt

v = t³ + t² + 2t + c

at, t = 0, v = 0

∴ c = 2

now at t=2, v= 8 + 4 + 4 + 2 = 18 m/s