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

Vectors

1. Which of the following are vectors?
   • 20 cm
   • 9.81 ms^-2 towards the centre of the earth
   • 5 km south-east
   • 500 ms^-1 on a bearing of 285.3°
2. 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?
3. If I travel at a velocity of 10 ms^-1 on a bearing of 030°, at what velocity am I travelling north and east?
4. An alternative method of writing vectors is in a column, as follows:

$\mathbf {a} ={\binom {x}{y}}$, 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. 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

1. In the following distance-time graph, what is the velocity 4 seconds after the beginning of the object's journey?

2a)Describe this person's movements. 2b)What is the velocity at 12 seconds?

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?