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?

An aircraft, starting from rest accelerates uniformly along a straight runway. It reaches a speed of$200 \mathrm{km} {\mathrm{h}}^{-1}$ and travels a distance of $1.4 \mathrm{km}$. What is the acceleration of the aircraft along the runway?

A ball is thrown with a velocity of $10 {\mathrm{ms}}^{-1}$at an angle of $30°$ to the horizontal. Air resistance has a negligible effect on the motion of the ball.

What is the velocity at the highest point of its path.

A trolley travels along a straight track. The variation with time $t$ of the velocity $v$ of the trolleyis shown in figure.

Which graph shows the variation with time of the acceleration $a$ of the trolley?