At the scene of an accident on a country road, police find skid marks stretching for $50 \mathrm{m}$. Tests on the road surface show that a skidding car decelerates at $6.5 \mathrm{m} {\mathrm{s}}^{-2}$. Was the car that skidded exceeding the speed limit of $25 \mathrm{m} {\mathrm{s}}^{-1}$$\left(90 \mathrm{km} {\mathrm{h}}^{-1}\right)$ on this road?

An egg falls off a table. The floor is $0.8 \mathrm{m}$ from the table-top. Calculate the time taken to reach the ground. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

An egg falls off a table. The floor is $0.8 \mathrm{m}$ from the table-top. Calculate the velocity of impact with the ground. $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

In chapter $1$, we looked at how to use a motion sensor to measure the speed and position of a moving object. Based on the similar methadology, suggest how a motion sensor could be used to determine $g$.

Find the x-and y-components of each of the vectors shown in Figure $2.29$.

Figure $2.29$.

In the example in 'Falling further, of the text book, calculate the time it will take for the stone to reach the foot of the cliff.

Note-In the example of 'Falling further' in example, it is given that the height of the cliff is $25 \mathrm{m}$.

The range of a projectile is the horizontal distance it travels before it reaches the ground. The greatest range is achieved if the projectile is thrown at $45°$ to the horizontal.

A ball is thrown with an initial velocity of $40 {\mathrm{ms}}^{-1}$. Calculate its greatest possible range when air resistance is considered to be negligible.

Could you easily teach somebody a proof of the equations of motion? How would you do this?