《Mechanics 1历年考试真题分类汇编》

Section A Velocity and Acceleration

（Chapter 1）

1．

A man runs in a straight line. He passes through a fixed point A with constant

velocity 7ms_1at time t = 0. At time t s his velocity is v ms_1. The diagram shows the graph of v against t for the period 0 ≤t ≤ 40. （02w）

(i) Show that the man runs more than 154m in the first 24 s. [2]

(ii)Given that the man runs 20m in the interval 20 ≤t ≤ 24, find how far he is from A when t = 40.[2]

2

The diagram shows the velocity-time graphs for the motion of two cyclists P and Q, who travel in the same direction along a straight path. Both cyclists start from rest at the same point O and both accelerate at 2ms?2 up to a speed of 10ms?1. Both then continue at a constant speed of 10ms?1.(03s)

Q starts his journey T seconds after P.

(i) Show in a sketch of the diagram the region whose area represents the

displacement of P, from O,at the instant when Q starts. [1]

Given that P has travelled 16m at the instant when Q starts, find

(ii) the value of T, [3]

(iii)the distance between P and Q when Q’s speed reaches 10ms?1. [2]

3

A boy runs from a point A to a point C. He pauses at C and then walks back towards

A until reaching the point B, where he stops. The diagram shows the graph of

v against t, where v ms?1 is the boy,s velocity at time t seconds after leaving

A. The boy runs and walks in the same straight line throughout. (04s)

(i) Find the distances AC and AB. [3]

(ii) Sketch the graph of x against t, where x metres is the boy,s displacement from A. Show clearly the values of t and x when the boy arrives at C, when he leaves C, and when he arrives at B. [3]

4

Particles P and Q start from points A and B respectively, at the same instant, and move towards each other in a horizontal straight line. The initial speeds of P and Q are 5ms?1 and 3ms?1 respectively. The accelerations of P and Q are constant and equal to 4ms?2 and 2ms?2 respectively (see diagram).（04w）

(i) Find the speed of P at the instant when the speed of P is 1.8 times the speed

of Q. [4]

(ii) Given that AB = 51 m, find the time taken from the start until P and Q meet.

5

The diagram shows the velocity-time graph for a lift moving between floors in

a building. The graph consists of straight line segments. In the first stage

the lift travels downwards from the ground floor for 5 s, coming to rest at

the basement after travelling 10 m. (05s)

(i) Find the greatest speed reached during this stage. [2]

The second stage consists of a 10 s wait at the basement. In the third stage,

the lift travels upwards until it comes to rest at a floor 34.5m above the basement,

arriving 24.5 s after the start of the first stage. The lift accelerates at 2ms

?2 for the first 3 s of the third stage, reaching a speed of V ms?1. Find

(ii) the value of V, [2]

(iii) the time during the third stage for which the lift is moving at constant speed, [3]

(iv) the deceleration of the lift in the final part of the third stage. [2]

6 A car travels in a straight line with constant acceleration a ms?2. It passes

the points A, B and C, in this order, with speeds 5ms?1, 7ms?1and 8ms?1respectively.

The distances AB and BC are d1 m and d2 m respectively.

(i) Write down an equation connecting (a) d1 and a,(b) d2 and a. [2]

(ii) Hence find d1 in terms of d2. [2]

7、 The diagram shows the displacement-time graph for a car’s journey. The graph

consists of two curved parts AB and CD, and a straight line BC. The line BC is

a tangent to the curve AB at B and a tangent to the curve CD at C. The gradient

of the curves at t = 0 and t = 600 is zero, and the acceleration of the car is constant for 0 < t < 80 and for 560 < t < 600. The displacement of the car is 400m when t = 80. (05w)

(i) Sketch the velocity-time graph for the journey. [3]

(ii) Find the velocity at t = 80. [2]

(iii) Find the total distance for the journey. [2]

(iv) Find the acceleration of the car for 0 < t < 80. [2]

8

The diagram shows the velocity-time graph for the motion of a small stone which falls vertically from rest at a point A above the surface of liquid in a container.

The downward velocity of the stone t s after leaving A is v ms?1. The stone hits the surface of the liquid with velocity7ms?1when t = 0.7. It reaches the bottom of the container with velocity 5ms?1 when

t = 1.2. （06s）

(i) Find

(a) the height of A above the surface of the liquid,

(b) the depth of liquid in the container.[3]

(ii) Find the deceleration of the stone while it is moving in the liquid. [2]

(iii)Given that the resistance to motion of the stone while it is moving in the liquid has magnitude 0.7N, find the mass of the stone. [3]

9 A train travels from A to B, a distance of 20 000m, taking 1000 s. The journey

has three stages. In the first stage the train starts from rest at A and

accelerates uniformly until its speed is V ms?1. In the second stage the train

travels at constant speed V ms?1 for 600 s. During the third stage of the journey

the train decelerates uniformly, coming to rest at B. （08w）

(i) Sketch the velocity-time graph for the train’s journey. [2]

(ii) Find the value of V. [3]

(iii) Given that the acceleration of the train during the first stage of the

journey is 0.15 ms?2, find the distance travelled by the train during the

third stage of the journey. [4]

10

A train starts from rest at a station and travels in a straight line until it

comes to rest again at the next station. The displacement-time graph above refers

to the journey. (01w)

(i) The speed of the train is constant from t = 120 to t = 440. Find this speed.

[2]

(ii) Given that the acceleration of the train is constant from t = o to

t= 120 and from t = 440 to t = 480, make a sketch of the velocity-time

graph for the journey, showing the maximum speed of the train. [3]