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Unit Four

Mechanics

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Chapter 15

Rectilinear Motion

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Objective

1

Uniform Rectilinear Motion

2

Uniform Accelerated rectilinear Motion

3

Uniform Decelerated rectilinear Motion

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Uniform Rectilinear Motion (URM)

Uniform Rectilinear Motion: when the speed is constant during motion.

The trajectory of the moving body is a straight line.
The distance covered during equal interval of time are equal.
The average speed between any two instants is equal the instantaneous speed and acceleration=0.

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Uniform Rectilinear Motion (URM)

Time equation Motion of URM:

If a body moves in positive sense with a speed V such that at the instant t0 =0 the body was at X0, then its position at instant t is:

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Uniform Rectilinear Motion (URM)

Time equation Motion: graphically

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Uniform Rectilinear Motion (URM)

Time equation Motion: graphically

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Uniform Rectilinear Motion (URM)

Example 1:

The position of a particle in terms of

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Uniform Rectilinear Motion (URM)

Solution of Example 1:

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Uniform Rectilinear Motion (URM)

Solution of Example 1:

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Uniform Rectilinear Motion (URM)

Solution of Example 1:

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Uniformly Accelerated Rectilinear Motion

UARM: when the speed of the body increases with time and the acceleration is constant.

The distance traveled during interval of time is not constant but increase with time.
The average and instantaneous speeds increases with time.
The acceleration(a) is constant over time.

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Uniformly Accelerated Rectilinear Motion

Its position is:

Its speed is:

Relation of V and x is:

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Uniformly Accelerated Rectilinear Motion

For V=at+V0

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Uniformly Accelerated Rectilinear Motion

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Uniformly Accelerated Rectilinear Motion

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Uniformly Accelerated Rectilinear Motion

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Uniformly Accelerated Rectilinear Motion

Example 2:

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Uniformly Accelerated Rectilinear Motion

Solution of Example 2:

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Uniformly Accelerated Rectilinear Motion

Solution of Example 2:

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Uniformly Decelerated Rectilinear Motion

Time equation Motion of UARM:

A body moves in positive sense with acceleration (a), knowing that at t0=0 the body passes by the point M0 of abscissa (X0) with a speed (V0), Then:

Its position at instant t is:

Its speed at instant t is:

Relation of V & x at t is:

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Uniformly Decelerated Rectilinear Motion

V = at +V0

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Uniformly Decelerated Rectilinear Motion

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Uniformly Decelerated Rectilinear Motion

Example 3:

A particle D moving on a straight line

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Uniformly Decelerated Rectilinear Motion

Solution of Example 3:

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Uniformly Decelerated Rectilinear Motion

Solution of Example 3:

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Grade 10 solving problems Physics

Exercise 1:

Find the speeds of the car V_A, V_Band V_C at point A, B and C.
Calculate the acceleration of the car along OA, AB and BC.

The graph below shows the variation of abscissa as a function of time for a moving body.

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Grade 10 solving problems Physics

What is the nature of the motion of the car in each phase.
Calculate the distance covered by the car in each phase (OA, AB and BC).

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Grade 10 solving problems Physics

Solution of Exercise 1:

Find the speeds of the car V_A, V_Band V_C at point A, B and C.

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Grade 10 solving problems Physics

Solution of Exercise 1:

Calculate the acceleration of the car along OA, AB and BC.

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Grade 10 solving problems Physics

Solution of Exercise 1:

What is the nature of the motion of the car in each phase.

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Grade 10 solving problems Physics

Solution of Exercise 1:

Calculate the distance covered by the car in each phase (OA, AB and BC).

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Grade 10 solving problems Physics

Solution of Exercise 1:

Calculate the distance covered by the car in each phase (OA, AB and BC).

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Grade 10 solving problems Physics

Solution of Exercise 1:

Calculate the distance covered by the car in each phase (OA, AB and BC).

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Grade 10 solving problems Physics

Exercise 2:

The recording of the motion of the puck is given below with time interval τ =20ms.

Compare the distance traveled by the puck in equal time interval.
Calculate the average speed of the puck between any two instants.

A puck thrown on a horizontal air table.

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Grade 10 solving problems Physics

Calculate the instantaneous speed for any instants. Conclude.
Calculate the average acceleration of the puck between any two instants.
What is the nature of motion.

Exercise 2:

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Grade 10 solving problems Physics

Solution of Exercise 2:

Compare the distance traveled by the puck in equal time interval.

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Grade 10 solving problems Physics

Solution of Exercise 2:

Calculate the average speed of the puck between any two instants.

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Grade 10 solving problems Physics

Solution of Exercise 2:

Calculate the instantaneous speed for any instants. Conclude.

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Grade 10 solving problems Physics

Solution of Exercise 2:

Calculate the average acceleration of the puck between any two instants.

What is the nature of motion.

Because the speed is constant over time and the acceleration is zero, then the motion is Uniform Rectilinear motion (URM).

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Grade 10 solving problems Physics

Exercise 3:

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Grade 10 solving problems Physics

Solution of Exercise 3:

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Grade 10 solving problems Physics

Solution of Exercise 3:

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Grade 10 solving problems Physics

Exercise 4:

Consider the trajectory of a moving puck on the air table; the points are recorded at instant separated by equal time interval τ=60ms. The scale is ¼.

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Grade 10 solving problems Physics

Exercise 4:

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Grade 10 solving problems Physics

Solution of Exercise 4:

τ=60ms. The scale is ¼.

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Grade 10 solving problems Physics

Solution of Exercise 4:

t(ms)	τ	2τ	3τ	4τ
V(m/s)	0.73	0.83	0.93	1.03

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Grade 10 solving problems Physics

Solution of Exercise 4:

Draw the graph that represents the variation of the velocity with respect to t.

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Grade 10 solving problems Physics

Solution of Exercise 4:

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Grade 10 solving problems Physics

Solution of Exercise 4:

Deduce the nature of the motion.

The velocity increases with time and the graph of velocity is Straight line; so the motion is UARM.

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Grade 10 solving problems Physics

Solution of Exercise 4:

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Grade 10 solving problems Physics

Solution of Exercise 4:

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Grade 10 solving problems Physics

Solution of Exercise 4:

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Quiz in physics (10 points)

Chapter 15: Rectilinear Motion

Time: 20 min

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Grade 10 Quiz in Physics Time: 20min

Consider the motion of a puck on a horizontal air table. Traces of its center of P are being recorded on the conduct sheet with a frequency of f=10Hz. The positions of P are given as follows:


	-2.4	-1.6	-0.8	0	0.8	1.6	2.4	3.2

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Grade 10 Quiz in Physics Time: 20min

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Grade 10 Quiz in Physics Time: 20min

Explain why the puck is moving in uniform rectilinear motion.
Give the numerical time equations of this motion.
Calculate the position of the puck at t=2s.

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Grade 10 Quiz in Physics Time: 20min

Solution of Quiz

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Grade 10 Quiz in Physics Time: 20min

Solution of Quiz

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Grade 10 Quiz in Physics Time: 20min

Solution of Quiz

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Grade 10 Quiz in Physics Time: 20min

Solution of Quiz

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Grade 10 Quiz in Physics Time: 20min

Solution of Quiz

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Grade 10 Quiz in Physics Time: 20min

Solution of Quiz

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Grade 10 Quiz in Physics Time: 20min

Solution of Quiz

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End of Chapter 15