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?

A motorway designer can assume that cars approaching a motorway enter a slip road with a velocity of $10 {\mathrm{ms}}^{-1}$ and reach a velocity of $30 {\mathrm{ms}}^{-1}$ before joining the motorway. Calculate the minimum length for the slip road, assuming that vehicles have an acceleration of $4.0 {\mathrm{ms}}^{-2}$.

A train is travelling at $50 {\mathrm{ms}}^{-1}$ when the driver applies the brakes and gives the train a constant deceleration of magnitude $0.50{\mathrm{ms}}^{-2}$ for$100\mathrm{s}$. Describe what happens to the train. Calculate the distance travelled by the train in $100 \mathrm{s}$.

A student measures the speed $\mathrm{v}$ of the trolley as it moves down the slope. The variation of $v$ with time $\mathrm{t}$ is shown in the graph.

Use the graph to find the velocity of the trolley, when $\mathrm{t}=0.70 \mathrm{s}$