The speed-time graphs for three vehicles X, Y, and Z are shown.

If x, y, and z are the distance travelled by X, Y, and Z respectively in 8 s, which of the following comparison is correct?

Question

The speed-time graphs for three vehicles X, Y, and Z are shown.

If x, y, and z are the distance travelled by X, Y, and Z respectively in 8 s, which of the following comparison is correct?

BlackTom AI · Accepted Answer

The question provides speed-time graphs for three vehicles X, Y, and Z and asks which distance comparison is correct after 8 s. Option 1: x = y < z To assess this, we need the areas under each speed-time curve up to t = 8 s, since distance is the integral of speed over time. From the graph, X travels with a speed increasing linearly from 0 to 10 m/s over 8 s, forming a right triangle with base 8 s and height 10 m/s. The area is (1/2) × 8 × 10 = 40 m. Y’s curve rises from 0 to 4 m/s over 4 s and then remains at 4 m/s from t = 4 s to t = 8 s, forming a right triangle (0 to 4 s) plus a rectangle (4 to 8 s). The triangle area is (1/2) × 4 × 4 = 8 m, and the rectangle area is 4 s × 4 m/s = 16 m, totaling 24 m. Z’s speed rises linearly from 0 to 6 m/s over 8 s, forming a triangle with base 8 s and height 6 m/s, giving area (1/2) × 8 × 6 = 24 m. Since 40 ≠ 24, the claim x = y is false and x < z is also false; thus this option is incorrect. Option 2: x > y > z From the calculated areas, x = 40 m, y = 24 m, z = 24 m. Here, y > z would require y’s distance to exceed z’s, but both y and z are 24 m, so y > z is false. Therefore this option is incorrect due to the inequality between y and z. Option 3: x > y = z With x = 40 m and y = z = 24 m, X covers more distance than both Y and Z, and Y and Z cover equal distances. This matches the numerical results derived from the areas under the speed-time graphs, making this option internally consistent with the graph. The reasoning hinges on comparing the triangle area for X against the combined triangle/rectangle area for Y and the triangle area for Z, which turn out to be 40 m, 24 m, and 24 m respectively. Option 4: x < y < z This would require X’s distance to be less than Y’s, and Y’s less than Z’s, which contradicts the calculated values (X is the largest, Y and Z are equal). Hence this option is incorrect. Summarizing the analyses: the numerical areas under the curves show X travels 40 m, while Y and Z each travel 24 m, so the relation is X greater than both Y and Z with Y equal to Z. The only option that matches this comparison pattern is the one stating x > y = z, while all other options fail due to incorrect equalities or orderings.

SPHY001 Graded Quiz 1 (Unit 1 and Unit 2)- Requires Respondus LockDown Browser

The speed-time graphs for three vehicles X, Y, and Z are shown. If x, y, and z are the distance travelled by X, Y, and Z respectively in 8 s, which of the following comparison is correct?

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