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Question

A student records the motion of a ball that travels from point Q to point R, then returns to point S, all along the same straight path. If the ball covers 70 meters to reach R from Q and then 30 meters from R to S, which best represents the physical difference between the total path length and displacement for this journey?

The correct answer is

The path length is the total distance travelled, while displacement is the net straight-line distance from Q to S.

Path length (distance) is the total length of the path actually travelled. Here the ball goes 70 m from Q to R and then 30 m back from R to S, so path length = 70 + 30 = 100 m.

Displacement is the shortest straight-line distance from the initial position to the final position. Since the ball comes back 30 m along the same line, S is 70 − 30 = 40 m from Q, so the displacement is 40 m from Q towards R.

This shows that displacement can never exceed path length, that the two are not equal when the motion reverses even on a straight line, and that it is displacement (not path length) that depends only on the initial and final positions.

Hence, the path length is the total distance travelled, while displacement is the net straight-line distance from Q to S.

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Similar Questions

  1. A speed - time graph for a car shows a straight line rising from 0 m/s at 0 s to 20 m/s at 5 s, then staying constant at 20 m/s until 10 s, and finally dropping to 0 m/s at 15 s. What is the total distance travelled by the car?

  2. In a distance-time graph, two vehicles are represented by two lines: one is a straight line inclined to the time axis, and the other is a curved line with increasing steepness. What does this suggest about the motion of the two vehicles?

  3. A train moves 60 km at 30 km/h, halts for 1h, and then covers 90 km at 45 km/h. What is the average speed over the entire journey?

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  5. In a distance-time graph, if the curve is NOT a straight line, then it represents _______.

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Important Questions from Motion

  1. An object is covering distance in direct proportion to the square of time elapsed. What conclusion can be drawn about the motion of the object?

  2. If the distance time graph of the motion of an object is a straight line but not parallel to the time axis, then it may be concluded that the object is moving with a:

  3. Vehicles have treaded tires so that it_______.

  4. What is the formula for momentum?

  5. Momentum of a given body is doubled. Its kinetic energy becomes (mass not changed)

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