19. Exercises - Versionshistorik

Ian den 19 november 2009 kl. 19.08

2009-11-19T19:08:55Z

← Äldre version		Versionen från 19 november 2009 kl. 19.08
Rad 163:		Rad 163:
	<div class="ovning">		<div class="ovning">

		+	An aeroplane moves so that at time <math>t</math>
		+	seconds its acceleration,
		+	<math>\mathbf{a}</math>
		+	<math>\text{m}{{\text{s}}^{-2}}</math>
		+	is given by:

		+	<math>\mathbf{a}=-2\mathbf{j}</math>
		+
		+	When
		+	<math>t=\text{ }0</math>
		+	the velocity of the aeroplane is (40<math>\mathbf{i}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>and its position vector is
		+	(400<math>\mathbf{j}</math>) metres.
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are directed east and north respectively.
		+
		+	a) Find the velocity of the aeroplane at time <math>t</math>.
		+
		+	b) Find the position vector of the particle at time <math>t</math>.
		+
		+	c) Find the time when the aeroplane is travelling south east.
		+
		+	d) Find the time when the aeroplane is due east of the origin.

	</div>{{#NAVCONTENT:Answer a\|Answer 19.8a\|Answer b\|Answer 19.8b\|Answer c\|Answer 19.8c\|Answer d\|Answer 19.8d\|Solution a\|Solution 19.8a\|Solution b\|Solution 19.8b\|Solution c\|Solution 19.8c\|Solution d\|Solution 19.8d}}		</div>{{#NAVCONTENT:Answer a\|Answer 19.8a\|Answer b\|Answer 19.8b\|Answer c\|Answer 19.8c\|Answer d\|Answer 19.8d\|Solution a\|Solution 19.8a\|Solution b\|Solution 19.8b\|Solution c\|Solution 19.8c\|Solution d\|Solution 19.8d}}

Ian den 19 november 2009 kl. 18.53

2009-11-19T18:53:53Z

← Äldre version		Versionen från 19 november 2009 kl. 18.53
Rad 133:		Rad 133:
	<div class="ovning">		<div class="ovning">

		+	A particle has mass 4 kg. It moves so that the resultant force,
		+	<math>\mathbf{F}</math>
		+	N, acting on it at time
		+	<math>t</math>
		+	seconds is given by:
		+
		+	<math>\mathbf{F}=12t\mathbf{i}+(6-5t)\mathbf{j}</math>
		+
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are perpendicular.
		+
		+	a) Find the acceleration of the particle.
		+
		+	b) Find the velocity of the particle at time
		+	<math>t</math>
		+	if it has an initial velocity
		+	of -8<math>\mathbf{i}</math> <math>\text{m}{{\text{s}}^{-1}}</math>.
		+
		+	c) Given that the initial position of the particle is (<math>90\mathbf{i}+20\mathbf{j}</math>) metres, find an expression for the position vector of the particle at time
		+	<math>t</math>.
		+
		+	d) Find the distance of the particle from the origin when
		+	<math>t=\text{ 2}0</math>.

Ian den 19 november 2009 kl. 18.43

2009-11-19T18:43:41Z

← Äldre version		Versionen från 19 november 2009 kl. 18.43
Rad 128:		Rad 128:

	</div>{{#NAVCONTENT:Answer a\|Answer 19.6a\|Answer b\|Answer 19.6b\|Solution a\|Solution 19.6a\|Solution b\|Solution 19.6b}}		</div>{{#NAVCONTENT:Answer a\|Answer 19.6a\|Answer b\|Answer 19.6b\|Solution a\|Solution 19.6a\|Solution b\|Solution 19.6b}}
		+
		+
		+	===Exercise 19.7===
		+	<div class="ovning">
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 19.7a\|Answer b\|Answer 19.7b\|Answer c\|Answer 19.7c\|Answer d\|Answer 19.7d\|Solution a\|Solution 19.7a\|Solution b\|Solution 19.7b\|Solution c\|Solution 19.7c\|Solution d\|Solution 19.7d}}
		+
		+
		+	===Exercise 19.8===
		+	<div class="ovning">
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 19.8a\|Answer b\|Answer 19.8b\|Answer c\|Answer 19.8c\|Answer d\|Answer 19.8d\|Solution a\|Solution 19.8a\|Solution b\|Solution 19.8b\|Solution c\|Solution 19.8c\|Solution d\|Solution 19.8d}}

Ian den 19 november 2009 kl. 18.25

2009-11-19T18:25:31Z

← Äldre version		Versionen från 19 november 2009 kl. 18.25
Rad 110:		Rad 110:

	b) Find the distance that the car travels during the 40 seconds.		b) Find the distance that the car travels during the 40 seconds.
-

	</div>{{#NAVCONTENT:Answer a\|Answer 19.5a\|Answer b\|Answer 19.5b\|Solution a\|Solution 19.5a\|Solution b\|Solution 19.5b}}		</div>{{#NAVCONTENT:Answer a\|Answer 19.5a\|Answer b\|Answer 19.5b\|Solution a\|Solution 19.5a\|Solution b\|Solution 19.5b}}
		+
		+
		+	===Exercise 19.6===
		+	<div class="ovning">
		+
		+	A car is moving along a straight road. The velocity of the car at time <math>t</math> seconds is
		+	<math>\left( 3{{t}^{2}}+2t+5 \right)</math>
		+	<math>\text{m}{{\text{s}}^{-2}}</math>.
		+
		+	a) Find an expression for the acceleration of the car at time <math>t</math>.
		+
		+	b) Find the total distance travelled by the car when
		+	<math>t=\text{ 1}0</math>
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 19.6a\|Answer b\|Answer 19.6b\|Solution a\|Solution 19.6a\|Solution b\|Solution 19.6b}}

Ian den 19 november 2009 kl. 18.18

2009-11-19T18:18:17Z

← Äldre version		Versionen från 19 november 2009 kl. 18.18
Rad 90:		Rad 90:

	c) Find the distance travelled by the car in the 20 second period.		c) Find the distance travelled by the car in the 20 second period.
-

	</div>{{#NAVCONTENT:Answer b\|Answer 19.4b\|Answer c\|Answer 19.4c\|Solution a\|Solution 19.4a\|Solution b\|Solution 19.4b\|Solution c\|Solution 19.4c}}		</div>{{#NAVCONTENT:Answer b\|Answer 19.4b\|Answer c\|Answer 19.4c\|Solution a\|Solution 19.4a\|Solution b\|Solution 19.4b\|Solution c\|Solution 19.4c}}
		+
		+
		+	===Exercise 19.5===
		+	<div class="ovning">
		+
		+	A van slows down from a speed of 20 <math>\text{m}{{\text{s}}^{-1}}</math>
		+	to 5 <math>\text{m}{{\text{s}}^{-1}}</math>
		+	in 40 seconds. At time <math>t</math>
		+	seconds the acceleration, <math>a</math>
		+	<math>\text{m}{{\text{s}}^{-2}}</math>
		+	is given by
		+	<math>a=-kt</math>, where
		+	<math>k</math> is a constant.
		+
		+	a) Find
		+	<math>k</math>.
		+
		+	b) Find the distance that the car travels during the 40 seconds.
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 19.5a\|Answer b\|Answer 19.5b\|Solution a\|Solution 19.5a\|Solution b\|Solution 19.5b}}

Ian den 19 november 2009 kl. 18.10

2009-11-19T18:10:36Z

← Äldre version		Versionen från 19 november 2009 kl. 18.10
Rad 65:		Rad 65:
	c) Find the distance that the dragster travels in the 10 seconds.		c) Find the distance that the dragster travels in the 10 seconds.

		+	</div>{{#NAVCONTENT:Answer b\|Answer 19.3b\|Answer c\|Answer 19.3c\|Solution a\|Solution 19.3a\|Solution b\|Solution 19.3b\|Solution c\|Solution 19.3c}}


-	</div>{{#NAVCONTENT:Answer b\|Answer 19.3b\|Answer c\|Answer 19.3c\|Solution a\|Solution 19.3a\|Solution b\|Solution 19.3b\|Solution c\|Solution 19.3c}}	+	===Exercise 19.4===
		+	<div class="ovning">
		+
		+	A car, of mass 1000 kg, accelerates for 20 seconds along a straight road. The graph below shows how the resultant force on the car varies with time as it accelerates.
		+
		+	[[Image:E19.4.GIF]]
		+
		+	a) Show that the acceleration,
		+	<math>a</math>
		+	<math>\text{m}{{\text{s}}^{-2}}</math>, at time <math>t</math>
		+	seconds is given by
		+
		+	<math>a=\frac{4t}{5}</math>
		+	for
		+	<math>0\le t\le 20.</math>
		+
		+
		+	b) Given that the velocity of the car is 8 <math>\text{m}{{\text{s}}^{-1}}</math>
		+	when it starts to accelerate, find an expression for the velocity of the car at time <math>t</math>
		+	seconds.
		+
		+	c) Find the distance travelled by the car in the 20 second period.
		+
		+
		+	</div>{{#NAVCONTENT:Answer b\|Answer 19.4b\|Answer c\|Answer 19.4c\|Solution a\|Solution 19.4a\|Solution b\|Solution 19.4b\|Solution c\|Solution 19.4c}}

Ian den 19 november 2009 kl. 17.43

2009-11-19T17:43:29Z

← Äldre version		Versionen från 19 november 2009 kl. 17.43
Rad 28:		Rad 28:
	c) How far does the cyclist travel in the 15 seconds?		c) How far does the cyclist travel in the 15 seconds?

		+	</div>{{#NAVCONTENT:Answer a\|Answer 19.1a\|Answer b\|Answer 19.1b\|Answer c\|Answer 19.1c\|Solution a\|Solution 19.1a\|Solution b\|Solution 19.1b\|Solution c\|Solution 19.1c}}


-	</div>{{#NAVCONTENT:Answer a\|Answer 19.1a\|Answer b\|Answer 19.1b\|Answer c\|Answer 19.1c\|Solution a\|Solution 19.1a\|Solution b\|Solution 19.1b\|Solution c\|Solution 19.1c}}	+	===Exercise 19.2===
		+	<div class="ovning">
		+
		+	The acceleration, <math>a</math>
		+	<math>\text{m}{{\text{s}}^{-2}}</math>, at time <math>t</math>
		+	seconds of a particle, which moves along a straight line, is given by:
		+
		+	<math>a=\frac{t}{25}</math>
		+	.
		+
		+	a) Given that the initial velocity of the particle is 2 <math>\text{m}{{\text{s}}^{-1}}</math>, find an expression for the velocity of the particle.
		+
		+	b) Find the distance that the particle travels in the first 50 seconds of its motion.
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 19.2a\|Answer b\|Answer 19.2b\|Solution a\|Solution 19.2a\|Solution b\|Solution 19.2b}}
		+
		+
		+	===Exercise 19.3===
		+	<div class="ovning">
		+
		+	A dragster starts at rest and experiences an acceleration that decreases uniformly from 8 <math>\text{m}{{\text{s}}^{-2}}</math> to zero over a period of 10 seconds. It moves along a straight race track.
		+
		+	a) Show that at time <math>t</math>
		+	seconds the acceleration, <math>a</math>
		+	<math>\text{m}{{\text{s}}^{-2}}</math>
		+	is given by:
		+
		+	<math>a=8-\frac{8t}{10}</math>.
		+
		+	b) Find the speed of the dragster when it stops accelerating at the end of the 10 seconds.
		+
		+	c) Find the distance that the dragster travels in the 10 seconds.
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer b\|Answer 19.3b\|Answer c\|Answer 19.3c\|Solution a\|Solution 19.3a\|Solution b\|Solution 19.3b\|Solution c\|Solution 19.3c}}

Ian den 19 november 2009 kl. 16.52

2009-11-19T16:52:34Z

← Äldre version		Versionen från 19 november 2009 kl. 16.52
Rad 6:		Rad 6:
	\| style="border-bottom:1px solid #797979" width="100%"\|		\| style="border-bottom:1px solid #797979" width="100%"\|
	\|}		\|}
		+
		+
		+	===Exercise 19.1===
		+	<div class="ovning">
		+
		+	The acceleration,
		+	<math>a</math>
		+	<math>\text{m}{{\text{s}}^{-2}}</math>, of the cyclist, at time
		+	<math>t</math>
		+	seconds is given by:
		+	<math>a=1-\frac{t}{15}</math>
		+	for
		+	<math>0\le t\le 15</math>.
		+
		+	The cyclist travels along a straight road.
		+
		+	a) Given that the cyclist starts at rest, find an expression for the velocity cyclist at time <math>t</math>.
		+
		+	b) What is the speed of the cyclist after 15 seconds?
		+
		+	c) How far does the cyclist travel in the 15 seconds?
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 19.1a\|Answer b\|Answer 19.1b\|Answer c\|Answer 19.1c\|Solution a\|Solution 19.1a\|Solution b\|Solution 19.1b\|Solution c\|Solution 19.1c}}

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2009-11-16T18:32:49Z

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