User:Inconspicuum/Physics (A Level)/Mechanics 1 Questions

Vectors
$$\mathbf{a} = \binom{x}{y}$$, where x and y are the vertical and horizontal components of the vector respectively. Express |a| and the angle between a and $$\tbinom{1}{0}$$ in terms of x and y.
 * 1) Which of the following are vectors?
 * 2) * 20 cm
 * 3) * 9.81 ms-2 towards the centre of the earth
 * 4) * 5 km south-east
 * 5) * 500 ms-1 on a bearing of 285.3°
 * 6) A displacement vector a is the resultant vector of two other vectors, 5 m north and 10 m south-east. What does a equal, as a displacement and a bearing?
 * 7) If I travel at a velocity of 10 ms-1 on a bearing of 030°, at what velocity am I travelling north and east?
 * 8) An alternative method of writing vectors is in a column, as follows:
 * 1) A more accurate method of modelling the trajectory of a ball is to include air resistance as a constant force F. How would this be achieved?

Graphs
2a)Describe this person's movements. 2b)What is the velocity at 12 seconds?
 * 1) In the following distance-time graph, what is the velocity 4 seconds after the beginning of the object's journey?
 * 1) In the following velocity-time graph, how far does the object travel between 7 and 9 seconds?
 * 1) What is the object's acceleration at 8 seconds?
 * 2) A car travels at 10ms-1 for 5 minutes in a straight line, and then returns to its original location over the next 4 minutes, travelling at a constant velocity. Draw a distance-time graph showing the distance the car has travelled from its original location.
 * 3) Draw the velocity-time graph for the above situation.
 * 4) The velocity of a ball is related to the time since it was thrown by the equation $$v = 30 - 9.8t\,$$. How far has the ball travelled after 2 seconds?

Kinematics

 * 1) A person accelerates from a speed of 1 ms-1 to 1.7 ms-1 in 25 seconds. How far has he travelled in this time?
 * 2) A car accelerates at a rate of 18 kmh-2 to a speed of 60 kmh-1, travelling 1 km in the process. How fast was the car travelling before it travelled this distance?
 * 3) A goose in flight is travelling at 4 ms-1. It accelerates at a rate of 1.5 ms-2 for 7 seconds. What is its new speed?
 * 4) How far does an aeroplane travel if it accelerates from 400 kmh-1 at a rate of 40 kmh-2 for 1 hour?

Forces and Power

 * 1) I hit a ball of mass 5g with a cue on a billiards table with a force of 20N. If friction opposes me with a force of 14.2N, what is the resultant acceleration of the ball away from the cue?
 * 2) A 10g ball rolls down a 1.2m high slope, and leaves it with a velocity of 4ms-1. How much work is done by friction?
 * 3) An electric train is powered on a 30kV power supply, where the current is 100A. The train is travelling at 90 kmh-1. What is the net force exerted on it in a forwards direction?