determine the total distance travelled (in meters) by the particle at time t = 4 s

Question

The acceleration of a particle is defined by the relation a = −15t (m/s2)Knowing that X = 24 m, and v = 29 m/s when t = 0, determine the total distance travelled (in meters) by the particle at time t = 4 s.

Answer 1

Velocity v(t) = ∫-15tdt = -15t²/2 + C; at t= 0 v(0) = C = 29; v(t) = -15t²/2 + 29;

x(t) = ∫(-15t²/2 + 29)dt = - 5t³/2 + 29t + C; at t = 0 x(0) = C = 24; x(t) = - 5t³/2 + 29t + 24;

V(t) = 0 t = 1.9664.

So, distance s = ∫₀^1.9664(- 15t²/2 + 29)dt + ∫_1.9664⁴(15t²/2 - 29)dt = 120.03 m