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.

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 time taken between the driver coming over the top of the hill and applying the breaks. Suggest whetherthis shows whether the driver was alert to the danger.

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.

The speed limit on the road is $100 \mathrm{km}/\mathrm{h}$. Determine whether the driver was breaking the speed limit.