Question

A particle, starting from rest, moves in a straight line, whose equation of motion is

given by s=5t3

-3t2+6. Find the displacement, velocity and acceleration of the particle

after 5 seconds​

Answer 1

Answer:

Explanation:

f(t) = s = 5t³ - 3t² + 6

Displacement after 5 seconds is given by f(5).

Therefore, s = f(5) = 5(5)³ - 3(5)² + 6 = 625 - 75 + 6 = 556 m

Velocity is given by ds/dt

v = ds/dt = d/dt(5t³-3t²+6) = 15t² - 6t

Velocity after 5 seconds = 15(5)² - 6(5) = 375 - 30 = 345 m/s

Acceleration is given by dv/dt.

a = dv/dt = d/dt(15t²-6t) = 30t - 6

Acceleration after 5 seconds = 30(5) - 6 = 150 - 6 = 144 m/s²