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4) A motor scooter and a van set off along a straight road. They both start from rest at the same time and level with each other. The scooter accelerates with constant acceleration until it reaches its top speed of 20m/s. It then maintains a constant speed of 20m/s. The van accelerates with constant acceleration for 10s until it reaches its top speed V m/s, V>20. It then maintains a constant speed of V m/s. The van draws level with the scooter when the scooter has been travelling for 40s at its top speed. The total distance travelled by each vehicle is then 850m.

a) Sketch on the same diagram the speed-time graphs of both vehicles to illustrate their motion from the time when they start to the time when the van overtakes the scooter.

b) Find the time for which the schooter is accerelating.

a) Sketch on the same diagram the speed-time graphs of both vehicles to illustrate their motion from the time when they start to the time when the van overtakes the scooter.

b) Find the time for which the schooter is accerelating.

Well the speed-time graph should be straight forward, they both start at the origin for a start.

The scooter will have a linear increase (as it's constant acceleration) up to speed=20.

The van will have a lower gradient on it's accelerating section (or it will catch up the scooter) and will finish at a speed higher than the 20.

For part b) You have to consider the properties of their travel that will be identical at the point that they draw level. Do you recall what the area under a speed-time graph represents?

The scooter will have a linear increase (as it's constant acceleration) up to speed=20.

The van will have a lower gradient on it's accelerating section (or it will catch up the scooter) and will finish at a speed higher than the 20.

For part b) You have to consider the properties of their travel that will be identical at the point that they draw level. Do you recall what the area under a speed-time graph represents?

Original post by Tomming

Well the speed-time graph should be straight forward, they both start at the origin for a start.

The scooter will have a linear increase (as it's constant acceleration) up to speed=20.

The van will have a lower gradient on it's accelerating section (or it will catch up the scooter) and will finish at a speed higher than the 20.

For part b) You have to consider the properties of their travel that will be identical at the point that they draw level. Do you recall what the area under a speed-time graph represents?

The scooter will have a linear increase (as it's constant acceleration) up to speed=20.

The van will have a lower gradient on it's accelerating section (or it will catch up the scooter) and will finish at a speed higher than the 20.

For part b) You have to consider the properties of their travel that will be identical at the point that they draw level. Do you recall what the area under a speed-time graph represents?

Yeah thanks I did it but not exactly sure if it was right

My answer to part a) was as follows

PART b I got 5 seconds

part c I got 21.3ms-1

Original post by AhmedDavid

Yeah thanks I did it but not exactly sure if it was right

My answer to part a) was as follows

PART b I got 5 seconds

part c I got 21.3ms-1

My answer to part a) was as follows

PART b I got 5 seconds

part c I got 21.3ms-1

Both of those values seem fine! Well done.

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