A particle moves along a straight line. Its velocity varies with time according to v(t) = 6 - 2t, where v is in m/s and t is in seconds. The particle is at x = 0 at t = 0. The total distance travelled by the particle during the interval 0 <= t <= 5 s is:
Options

Question

A particle moves along a straight line. Its velocity varies with time according to v(t) = 6 - 2t, where v is in m/s and t is in seconds. The particle is at x = 0 at t = 0. The total distance travelled by the particle during the interval 0 <= t <= 5 s is:

Options

G1 Physics · Accepted Answer

The particle changes direction when v = 0: 6 - 2t = 0, so t = 3 s. From 0 to 3 s, distance = integral of (6 - 2t) dt = [6t - t^2]_0^3 = 9 m. From 3 to 5 s, displacement = [6t - t^2]_3^5 = -4 m, so distance = 4 m. Total distance = 9 + 4 = 13 m. Hence, option B is correct.