A toy car accelerated from rest for 2.8 seconds, then continued at its maximum speed of 1.8 m s-1 until 8.2 seconds, then put on its brakes and decelerated to a stop in 12.5 seconds. Its motion is plotted on the graph below. How far did it travel when it accelerated ($ t_1 $)? Give your answer to two decimal places.

Question

BlackTom AI · Accepted Answer

First, identify the phase of motion for t = t1 where the car is accelerating from rest. The car starts from rest and reaches a maximum speed of 1.8 m/s in 2.8 s, so the acceleration is constant during this interval: a = Δv/Δt = 1.8 / 2.8 ≈ 0.642857 m/s^2.
Next, compute the distance traveled during this acceleration phase using the kinematics formula for uniformly accelerated motion starting from rest: s = (1/2) a t^2.
Plugging in the values: s = 0.5 × 0.642857 × (2.8)^2. Since (2.8)^2 = 7.84 and 0.5 × 0.642857 ≈ 0.3214285, the product is s ≈ 0.3214285 × 7.84 ≈ 2.519999 ≈ 2.52 m when rounded to two decimals.
Therefore, the distance covered during the acceleration period t1 is about 2.52 m. 
Note: If one checks consistency with the graph, the triangular/linear rise corresponds to this initial acceleration region, and the plateau thereafter corresponds to the constant speed before deceleration.

MUF0121 Physics Unit 1 - Semester 2, 2025 2.10 Graphical analysis of motion

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MUF0121 Physics Unit 1 - Semester 2, 2025 2.10 Graphical analysis of motion

查看解析

登录即可查看完整答案

类似问题

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

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。