Question

A particle P is projected from the origin O so that it moves along the x-axis. At time t after projection, the velocity of the particle v is given by v = 3t^2 -24t +45. ) Find an expression for the displacement of P in the first 3 seconds of its motion using calculus(integration).

Answer 1

x = t³ − 12t² + 45t

Step-by-step explanation:

Position is the integral of velocity.

x = ∫ v dt

x = ∫ (3t² − 24t + 45) dt

x = t³ − 12t² + 45t + C

The particle is originally at the origin, so at t = 0, x = 0.

0 = (0)³ − 12(0)² + 45(0) + C

0 = C

x = t³ − 12t² + 45t