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, restate the given data from the problem to anchor the calculation: the toy car accelerates from rest for t1 = 2.8 s to reach a maximum speed of 1.8 m/s, then continues at that speed until t = 8.2 s, and finally brakes to a stop in 12.5 s. The question asks for the distance traveled during the acceleration phase (the interval from t = 0 to t = t1).

During uniform acceleration from rest to a final speed v over time t1, the relationship between final velocity, acceleration, and time is v = a t1. The distance traveled in this accelerating phase is given by d = (1/2) a t1^2. Substituting a = v / t1 into the distance formula gives d = (1/2) (v / t1) t1^2 = (1/2) v t1.

From the problem, the final speed after the acceleration phase is v = 1.8 m/s and the duration of acceleration is t1 = 2.8 s. Plugging these values into d = (1/2) v t1 yields d = (1/2) × 1.8 × 2.8.

Compute step by step: (1/2) × 1.8 = 0.9, then 0.9 × 2.8 = 2.52. An alternative route is to compute using d = 0.5 a t1^2 with a = v / t1 = 1.8 / 2.8, giving d = 0.5 × (1.8 / 2.8) × (2.8)^2 = 0.9 × 2.8 = 2.52, confirming consistency.

Thus, the distance covered during the acceleration phase is 2.52 meters.

Note: This calculation relies only on the kinematics of constant acceleration from rest to a known speed over a known time, independent of the subsequent motion (constant speed and braking) which would affect total distance but not the distance during the initial acceleration.

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

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单

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。