Question pattern: Directed position, distance & displacement
Original question 1 of 2 in this pattern
Directed journey on a coordinate line
Positions along a straight road are measured from an origin, with east taken as positive. A survey vehicle starts at x = −120 m, travels to x = +260 m in 50 s, and then travels to x = −40 m in a further 40 s.
Calculate for the complete 90 s journey:
a) the total distance travelled;
b) the displacement;
c) the average speed;
d) the average velocity, including its direction.
Worked answer
Solution
- Step 1
First-leg distance:
|260 - (-120)| = 380 m; second-leg distance:|-40 - 260| = 300 m. - Step 2
Total distance:
380 + 300 = 680 m. - Step 3
Displacement:
-40 - (-120) = +80 m, so the displacement is 80 m east. - Step 4
Average speed:
680 / 90 = 7.56 m s⁻¹ ≈ 7.6 m s⁻¹. - Step 5
Average velocity:
+80 / 90 = +0.889 m s⁻¹ ≈ 0.89 m s⁻¹, directed east.
Final answer
Distance = 680 m; displacement = 80 m east; average speed = 7.6 m s⁻¹; average velocity = 0.89 m s⁻¹ east.
Common mistake
Adding signed coordinate changes when calculating total distance.
Concepts tested
- distance
- displacement
- average speed
- average velocity
- sign convention
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