The figure shows the v-t graph of a truck moving on the road. The distance travelled in the first 8 seconds is

Question

BlackTom AI · Accepted Answer

The question asks for the distance travelled in the first 8 seconds, which is the area under the velocity-time (v-t) graph from t = 0 to t = 8 s.
Option 1 (15 m): This would correspond to a much smaller area, since the velocity is zero at t = 0 and increases linearly, so the area up to 8 s cannot be as low as 15 m.
Option 2 (30 m): Though closer, 30 m is still too small given the velocity reaches 12 m/s by t = 8 s (see below). The area under a linearly increasing v-t graph grows more than linearly with time; 30 m would require a much lower average speed than what the graph implies.
Option 3 (120 m): This would require an average velocity of 15 m/s over 8 s, which is impossible here because the velocity at t = 8 s is only 12 m/s (and the velocity starts from 0). Therefore 120 m is too large.
Option 4 (60 m): This is closer to the correct value but still not exact; we will see why it’s not correct when we compute precisely.

To compute accurately, note the graph shows a straight line from (0, 0) to (10 s, 15 m/s). The velocity at time t is v(t) = (15/10) t = 1.5 t for 0 ≤ t ≤ 10. The distance traveled from 0 to 8 s is the area under this line from 0 to 8:
- Using the triangle area method: the velocity at t = 8 s is v(8) = 1.5 × 8 = 12 m/s. The average velocity over 0–8 s is (0 + 12)/2 = 6 m/s. Distance = average velocity × time = 6 × 8 = 48 m.
- Alternatively, integrate: ∫(0 to 8) 1.5 t dt = 1.5 × (t^2/2) |0^8 = 0.75 × 64 = 48 m.
Thus, the exact distance traveled in the first 8 seconds is 48 m. The provided options do not include 48 m. The statement in the given answer field acknowledges that none of the options match the calculated distance, noting that 60 m is the closest but not accurate.

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

The figure shows the v-t graph of a truck moving on the road. The distance travelled in the first 8 seconds is

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

The figure shows the v-t graph of a truck moving on the road. The distance travelled in the first 8 seconds is

查看解析

登录即可查看完整答案

类似问题

The graph shows the speed of a car travelling along a road during heavy traffic. The car's displacement (in metres) can be calculated from the area under this graph. What is it? Give your answer to one significant figure.

The graph shows the speed of a remote controlled toy car travelling along a race track. The car's displacement (in metres) can be calculated from the area under this graph. What is it? Give your answer to 3 significant figures.

The graph shows the speed of a remote controlled toy car travelling along a race track. The car's displacement (in metres) can be calculated from the area under this graph. What is it? Give your answer to 3 significant figures.

总行驶距离是多少？（只写数值，不写单位）[Fill in the blank],米 如果您无法查看此图像，请单击此处。

Which line has no acceleration? If you cannot view this image, click here.

What is the total distance travelled? (only write the numerical value, no unit) [Fill in the blank], m If you cannot view this image, click here.

更多留学生实用工具

希望你的学习变得更简单

总行驶距离是多少？（只写数值，不写单位）[Fill in the blank],米如果您无法查看此图像，请单击此处。