91影视

You can use the kinematic equations to solve questions related to objects moving with uniform acceleration during their motion.

If 鈥�u鈥� is the initial velocity of an object of mass 鈥�尘鈥�which is moving with uniform acceleration 鈥�补鈥� and attains final velocity 鈥�v鈥� in time 鈥�t鈥� then the kinematics equation of motion connecting these variables can be written as:

$v=u+at$

The speed limit of the rod is:

$\begin{array}{c}v=40\mathrm{km}/\mathrm{h}\\ =\left(40\mathrm{km}/\mathrm{h}\right)脳\left(\frac{1000\mathrm{m}}{1\mathrm{km}}\right)脳\left(\frac{1\mathrm{h}}{3600s}\right)\\ =11.11\mathrm{m}/\mathrm{s}\end{array}$

You are driving at the speed limit. Therefore, the speed of your car is $v=11.11\mathrm{m}/\mathrm{s}$.

You are at a distance of 10.0 m from the spotlight. According to the figure, in order to reach the third stoplight, you have to cover the following distance:

$\begin{array}{c}x=10+15+50+15+70\\ =160\mathrm{m}\end{array}$

Since you are moving at a constant speed; therefore, the time taken to cover this distance will be:

$\begin{array}{c}\mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}}\\ t=\frac{x}{v}\\ =\frac{160\mathrm{m}}{11.11\mathrm{m}/\mathrm{s}}\\ =14.40\mathrm{s}\end{array}$

Thus, the time needed to reach the third stoplight is 14.40 s. However, lights will remain green for 13.0 s only. Therefore, you cannot pass through all three stoplights without being stopped.

Another car starts its journey from the first stoplight. Thus, it has to travel a distance of 150 m in order to reach the third stoplight.

The initial velocity of the car is $u=0\mathrm{m}/\mathrm{s}$.

The acceleration of the car to reach the speed limit (i.e., $v\text{'}=11.11\mathrm{m}/\mathrm{s}$) is $a=2.00\mathrm{m}/{\mathrm{s}}^2$.

Let $t\text{'}$be the time taken by the car to reach the speed limit from rest.

Using the equation of motion, you will get:

$\begin{array}{c}v\text{'}=u+at\text{'}\\ t\text{'}=\frac{v\text{'}-u}{a}\\ =\frac{\left(11.11-0\right)\mathrm{m}/\mathrm{s}}{2.00\mathrm{m}/{\mathrm{s}}^2鈥�}\\ =5.55\mathrm{s}\end{array}$

Thus,the time needed by another car to reach the speed limit is 5.55 s.

Use the equation of motion to find the distance $s\text{'}$covered by the car to attain the speed limit starting from rest.

$\begin{array}{c}{\left(v\text{'}\right)}^2-u^2=2as\text{'}\\ {\left(11.11\mathrm{m}/\mathrm{s}\right)}^2-{\left(0\mathrm{m}/\mathrm{s}\right)}^2=2\left(2.00\mathrm{m}/\mathrm{s}\right)s\text{'}\\ s\text{'}=30.86\mathrm{m}\end{array}$

Thus, in order to reach the third stoplight, the car has to cover a distance of $150\mathrm{m}-30.86\mathrm{m}=119.14\mathrm{m}$.

If $t\text{'}\text{'}$is the time taken by the other car in order to cover the remaining distance of 119.14 m at a constant speed of $11.11\mathrm{m}/\mathrm{s}$, then:

$\begin{array}{c}t\text{'}\text{'}=\frac{119.14\mathrm{m}}{11.11\mathrm{m}/\mathrm{s}}\\ =10.75\mathrm{s}\end{array}$

Thus, the total time taken by the other car to reach the third stoplight is:

$\begin{array}{c}t\text{'}+t\text{'}\text{'}=\left(5.55+10.75\right)鈥�\mathrm{s}\\ =16.3\mathrm{s}\end{array}$

However, lights will only remain green for 13.0 s, and the second car requires 16.3 s to reach the third stoplight. Therefore, the second car cannot pass through all three stoplights without being stopped. It cannot pass the third stoplight by$\mathbf{16}\mathbf{.}\mathbf{3}\mathbf{s}-\mathbf{13}\mathbf{.}\mathbf{0}\mathbf{s}=\mathbf{3}\mathbf{.}\mathbf{3}\mathbf{s}$.