Chapter 1

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.

A car starts from rest at the point A and moves in a straight line with constant acceleration for 20 seconds until it reaches the point B. The speed of the car at B is 30 m s. Calculate (a) the acceleration of the car, (b) the speed of the car as it passes the point C, where C is between A and B and AC = 40 m. (OCR)

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A car starts from rest at the point A and moves in a straight line with constant acceleration for 20 seconds until it reaches the point B.

A car starts from rest at the point A and moves in a straight line with constant acceleration for 20 seconds until it reaches the point B.

A train is slowing down with constant deceleration. It passes a signal at A, and after successive intervals of 40 seconds it passes points B and C, where AB = 1800 m and BC= 1400 m. (a) How fast is the train moving when it passes A? (b) How far from A does it come to a stop?

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A train is slowing down with constant deceleration. It passes a signal at A, and after successive intervals of 40 seconds it passes points B and C, where AB = 1800 m and BC= 1400 m.

A train is slowing down with constant deceleration. It passes a signal at A, and after successive intervals of 40 seconds it passes points B and C, where AB = 1800 m and BC= 1400 m.

A roller-skater increases speed from 4 m/s to 10 ms in 10 seconds at a constant rate. (a) What is her average velocity over this period? (b) For what proportion of the time is she moving at less than her average velocity? (c) For what proportion of the distance is she moving at less than her average velocity?

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A roller-skater increases speed from 4 m/s to 10 ms in 10 seconds at a constant rate. (a) What is her average velocity over this period?

A roller-skater increases speed from 4 m/s to 10 ms in 10 seconds at a constant rate. (a) What is her average velocity over this period?

A motorbike and a car are waiting side by side at traffic lights. When the lights turn to green, the motorbike accelerates at 24 m s2 up to a top speed of 20 m sTM, and the car accelerates at 1 ms2 up to a top speed of 30 m s. Both then continue to move at constant speed. Draw (t,v) graphs for each vehicle, using the same axes, and sketch the (t,s) graphs. (a) After what time will the motorbike and the car again be side by side? (b) What is the greatest distance that the motorbike is in front of the car?

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A motorbike and a car are waiting side by side at traffic lights. When the lights turn to green, the motorbike accelerates at 24 m s2 up to a top speed of

A motorbike and a car are waiting side by side at traffic lights. When the lights turn to green, the motorbike accelerates at 24 m s2 up to a top speed of

A car comes to a stop from a speed of 30 m s in a distance of 804 m. The driver brakes so as to produce a deceleration of m s2 to begin with, and then brakes harder to produce a deceleration of ms2. Find the speed of the car at the instant when the deceleration is increased, and the total time the car takes to stop.

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A car comes to a stop from a speed of 30 m s in a distance of 804 m. The driver brakes so as to produce a deceleration of m s2 to begin with,

A car comes to a stop from a speed of 30 m s in a distance of 804 m. The driver brakes so as to produce a deceleration of m s2 to begin with,

A car rounds a bend at 10 ms^-1, and then accelerates at 1/2ms^-2 along a straight stretch of road. There is a junction 400 m from the bend. When the car is 100 m from the junction, the driver brakes and brings the car to rest at the junction with constant deceleration. Draw a (t,v) graph to illustrate the motion of the car. Find how fast the car is moving when the brakes are applied, and the deceleration needed for the car to stop at the junction.

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A car rounds a bend at 10 ms^-1, and then accelerates at 1/2ms^-2 along a straight stretch of road. There is a junction 400 m from the bend.

A car rounds a bend at 10 ms^-1, and then accelerates at 1/2ms^-2 along a straight stretch of road. There is a junction 400 m from the bend.

The figure shows a map of the railway line from Aytown to City. The timetable is based on the assumption that the top speed of a train on this line is 60 km per hour; that it takes 3 minutes to reach this speed from rest, and 1 minute to bring the train to a stop, both at a constant rate; and that at an intermediate station 1 minute must be allowed to set down and pick up passengers. How long must the timetable allow for the whole journey (a) for trains which don’t stop at Beeburg, (b) for trains which do stop at Beeburg?

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The figure shows a map of the railway line from Aytown to City. The timetable is based on the assumption that the top speed of a train on this line is 60 km per hour

The figure shows a map of the railway line from Aytown to City. The timetable is based on the assumption that the top speed of a train on this line is 60 km per hour

Two villages are 900 metres apart. A car leaves the first village travelling at 15 ms and accelerates atm s2 for 30 seconds. How fast is it then travelling, and what distance has it covered in this time? The driver now sees the next village ahead, and decelerates so as to enter it at 15 m s1 What constant deceleration is needed to achieve this? How much time does the driver save. by accelerating and decelerating, rather than covering the whole distance at 15 m s1?

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Two villages are 900 metres apart. A car leaves the first village travelling at 15 ms and accelerates atm s2 for 30 seconds.

Two villages are 900 metres apart. A car leaves the first village travelling at 15 ms and accelerates atm s2 for 30 seconds.