Miscellaneous Exercise 1

If a ball is placed on a straight sloping track and then released from rest, the distances that it moves in successive equal intervals of time are found to be in the ratio 1:3:5:7:…. Show that this is consistent with the theory that the ball rolls down the track with constant acceleration.

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If a ball is placed on a straight sloping track and then released from rest, the distances that it moves in successive equal intervals of time are found to be in the ratio 1:3:5:7:....

If a ball is placed on a straight sloping track and then released from rest, the distances that it moves in successive equal intervals of time are found to be in the ratio 1:3:5:7:….

A train travels from a station P to the next station Q, arriving at Q exactly 5 minutes after leaving P. The (t,v) graph for the train’s journey is approximated by three straight line segments, as shown in the figure. (i) Write down the acceleration of the train during the first minute of the journey. (ii) Find the distance from P to Q.

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A train travels from a station P to the next station Q, arriving at Q exactly 5 minutes after leaving P. The (t,v) graph for the train's journey is approximated by three straight line segments, as shown in the figure. (i) Write down the acceleration of the train during the first minute of the journey. (ii) Find the distance from P to Q.

A train travels from a station P to the next station Q, arriving at Q exactly 5 minutes after leaving P. The (t,v) graph for the train’s journey is approximated by three straight line segments, as shown in the figure. (i) Write down the acceleration of the train during the first minute of the journey. (ii) Find the distance from P to Q.

A man is running for a bus at 3 m s. When he is 100 m from the bus stop, the bus passes him going at 8 m s1. If the deceleration of the bus is constant, at what constant rate should the man accelerate so as to arrive at the bus stop at the same instant as the bus?

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A man is running for a bus at 3 m s. When he is 100 m from the bus stop, the bus passes him going at 8 m s1. If the deceleration of the bus is constant, at what constant rate should the man accelerate

A man is running for a bus at 3 m s. When he is 100 m from the bus stop, the bus passes him going at 8 m s1. If the deceleration of the bus is constant, at what constant rate should the man accelerate

Two runners, Ayesha and Fatima, are leading the field in a long-distance race. They are both running at 5 ms, with Ayesha 10 m behind Fatima. When Fatima is 50 m from the tape, Ayesha accelerates but Fatima doesn’t. What is the least acceleration Ayesha must produce to overtake Fatima? If instead Fatima accelerates at 0.1 m s2 up to the tape, what is the least acceleration Ayesha must produce?

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Two runners, Ayesha and Fatima, are leading the field in a long-distance race. They are both running at 5 ms, with Ayesha 10 m behind Fatima.

Two runners, Ayesha and Fatima, are leading the field in a long-distance race. They are both running at 5 ms, with Ayesha 10 m behind Fatima.

A car is waiting at traffic lights with a van behind it. There is a 1 metre gap between them. When the lights turn green, the car accelerates at 1.5 ms-2 until it reaches a speed of 15 m/s; it then proceeds at this speed. The van does the same, starting when the gap between the vehicles is 4 metres. Find a formula for the distance travelled by the car in the first seconds (0≤t≤10), and hence the time interval between the car starting and the van starting. Find also the distance between the vehicles when they are both going at 15 m /s. (OCR)

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A car is waiting at traffic lights with a van behind it. There is a 1 metre gap between them.

A car is waiting at traffic lights with a van behind it. There is a 1 metre gap between them.

As a car passes the point A on a straight road, its speed is 10 m s. The car moves with constant acceleration am s2 along the road for T seconds until it reaches the point B, where its speed is V m s1. The car travels at this speed for a further 10 seconds, when it reaches the point C. From C it travels for a further T seconds with constant acceleration 3a ms2 until it reaches a speed of 20 m s1 at the point D. Sketch the (r,v) graph for the motion, and show that V = 12.5. Given that the distance between A and D is 675 m, find the values of a and T. (OCR)

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As a car passes the point A on a straight road, its speed is 10 m s.

As a car passes the point A on a straight road, its speed is 10 m s.

A motorist travelling at u ms^-1 joins a straight motorway. On the motorway she travels with a constant acceleration of 0.07 m s2 until her speed has increased by 2.8 m s1. (a) Calculate the time taken for this increase in speed. (b) Given that the distance travelled while this increase takes place is 1050 m, find u. (OCR)

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A motorist travelling at u ms^-1 joins a straight motorway. On the motorway she travels with a constant acceleration of 0.07 m s2 until her speed has increased by 2.8 m s1.

A motorist travelling at u ms^-1 joins a straight motorway. On the motorway she travels with a constant acceleration of 0.07 m s2 until her speed has increased by 2.8 m s1.