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 $\mathrm{t}=0.70 \mathrm{s}$

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.

Show the acceleration of the trolley varies between $t=0 and t=1.0 s$. Explain your answer by reference to the graph.

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.

Determine the distance travelled by the trolley between $t=0.60 and t=0.8 s$. 

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.

The student obtained the reading for $\mathrm{v}$ using a motion sensor. The readings may have random errors and systematic errors. Explain how these errors affect the velocity-time graph.

A car driving at speed$\mathrm{v}$ on a straight road. He comes over a hill to find a tree fallen on the road ahead. He immediately breaks hard but travels a distance of $60 \mathrm{m}$ at speed $\mathrm{v}$ before the breaks are applied. The skid marks left on the road by the wheels of the car are of length $140 \mathrm{m}$ as shown. The police investigate whether the driver was speeding and establish that the car decelerates at $2 {\mathrm{ms}}^{-2}$ during the skid.

 Determine the initial speed of the car before the breaks are applied.