Theory question 118
DynamicsThe displacement S metres of the particle from a fixed point O at time t seconds is given by S = t2 − 6t + 5.
(a) On a graph sheet, draw a displacement-time graph for the interval 0 ≤ t ≤ 6.
(b) From the graph, find the: (i) time at which the velocity is zero; (ii) average velocity over the interval 0 ≤ t ≤ 4; (iii) total distance covered in the interval 0 ≤ t ≤ 5.
Show the model answer
Model answer
(a) t: 0, 1, 2, 3, 4, 5, 6; S: 5, 0, −3, −4, −3, 0, 5. Plot a smooth U-shaped curve.
(b)(i) Velocity is zero at the lowest point, t = 3 s.
(ii) (S(4) − S(0))/4 = (−3 − 5)/4 = −2 ms⁻¹.
(iii) From S = 5 to −4 (9 m) then back to 0 (4 m): 13 m.
Explanation
Distance counts both directions; displacement does not.