A car is travelling along a straight, flat road. The velocity, km h, of the car and its position, kilometres, are measured from the position on the road where  .

The velocity and the position of the car are related by  , where    and  .

A speed detection device is positioned to detect the speed of a car as it passes the position  . The speed limit on the road is 40 km h.

The speed detection device will be activated if the car is travelling at 10% or more above the speed limit.

1. Determine, with evidence, whether the speed detection device will be activated.   (1 mark)
   

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2. Find the acceleration of the car, in km h, when  .
3. Give your answer in the form  , where  .   (3 marks)
   

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A body moves in a straight line so that when its displacement from a fixed origin is metres, its acceleration, , is . The body accelerates from rest and its velocity, , is equal to as it passes through the origin. The body then comes to rest again.

Find in terms of for this interval.  (4 marks)

A particle moves along a straight line. When the particle is m from a fixed point , its velocity, m s, is given by

, where  .

1. Find the acceleration of the particle, in m s, when  .   (2 marks)

2. Find the value that the velocity of the particle approaches as becomes very large.   (1 mark)

The velocity, ms, of a particle at time    seconds and at position    metre from the origin is  .

The acceleration of the particle, in , when    is

A variable force acts on a particle, causing it to move in a straight line. At time seconds, where  , its velocity metres per second and position metres from the origin are such that  .

The acceleration of the particle, in ms⁻², can be expressed as

A body is moving in a straight line and, after    seconds, it is metres from the origin and travelling at  ms.

Given that  , and that    where  , the equation for in terms of    is

A particle moves in a straight line. At time    seconds, where  , its displacement metres from the origin and its velocity    metres per second are such that  .

If    initially, then    is equal to

A body moves in a straight line such that its velocity    is given by  , where metres is its displacement from the origin.

The acceleration of the body in   is given by

The velocity, m/s, of a body when it is metres from a fixed point is given by

Find an expression for the acceleration of the body in terms of in simplest form.  (3 marks)

The acceleration, in , of a particle moving in a straight line is given by  , where metres is its displacement from a fixed origin .

If the particle is at rest where  , the speed of the particle, in , where    is

A.           

B.     

C.         

D.     

E.