18. Exercises - Versionshistorik

Ian den 17 november 2009 kl. 14.48

Ian — Tue, 17 Nov 2009 14:48:42 GMT

← Äldre version		Versionen från 17 november 2009 kl. 14.48
Rad 198:		Rad 198:
	d) Show that the acceleration of the boat is constant and state the direction of the acceleration.		d) Show that the acceleration of the boat is constant and state the direction of the acceleration.

		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.8a\|Answer b\|Answer 18.8b\|Answer c\|Answer 18.8c\|Answer d\|Answer 18.8d\|Solution a\|Solution 18.8a\|Solution b\|Solution 18.8b\|Solution c\|Solution 18.8c\|Solution d\|Solution 18.8d}}


-	</div>{{#NAVCONTENT:Answer a\|Answer 18.8a\|Answer b\|Answer 18.8b\|Answer c\|Answer 18.~~8c\|Answer d\|Answer 18.8d~~\|Solution a\|Solution 18.8a\|Solution b\|Solution 18.8b\|Solution c\|Solution 18.~~8c\|Solution d\|Solution 18.8d~~}}	+	===Exercise 18.9===
		+	<div class="ovning">
		+
		+	The position vector,
		+	<math>\mathbf{r}</math>
		+	metres, of a particle at time
		+	<math>t</math>
		+	seconds is given by:
		+
		+	<math>\mathbf{r}=({{t}^{2}}-t+5)\mathbf{i}+({{t}^{3}}-12{{t}^{2}}+45t+17)\mathbf{j}</math>
		+
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are horizontal and vertical unit vectors respectively. The mass of the particle is 3 kg.
		+
		+	a) Find an expression for the velocity of the particle at time
		+	<math>t</math>.
		+
		+	b) Find the times when the particle is moving parallel to the ground.
		+
		+	c) Find an expression for the resultant force acting on the particle at time
		+	<math>t</math>.
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.9a\|Answer b\|Answer 18.9b\|Answer c\|Answer 18.9c\|Solution a\|Solution 18.9a\|Solution b\|Solution 18.9b\|Solution c\|Solution 18.9c}}

Ian den 17 november 2009 kl. 14.43

Ian — Tue, 17 Nov 2009 14:43:03 GMT

← Äldre version		Versionen från 17 november 2009 kl. 14.43
Rad 172:		Rad 172:

	c) Show that the acceleration of the aeroplane is constant and state its magnitude.		c) Show that the acceleration of the aeroplane is constant and state its magnitude.
-


	</div>{{#NAVCONTENT:Answer a\|Answer 18.7a\|Answer b\|Answer 18.7b\|Answer c\|Answer 18.7c\|Solution a\|Solution 18.7a\|Solution b\|Solution 18.7b\|Solution c\|Solution 18.7c}}		</div>{{#NAVCONTENT:Answer a\|Answer 18.7a\|Answer b\|Answer 18.7b\|Answer c\|Answer 18.7c\|Solution a\|Solution 18.7a\|Solution b\|Solution 18.7b\|Solution c\|Solution 18.7c}}
		+
		+
		+	===Exercise 18.8===
		+	<div class="ovning">
		+
		+	A boat moves so that its position vector,
		+	<math>~\mathbf{r}</math>
		+	metres, at time
		+	<math>t</math>
		+	seconds is given by
		+	<math>\mathbf{r}=\left( 2t-\frac{{{t}^{2}}}{10} \right)\mathbf{i}+2t\mathbf{j}</math>
		+
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are directed east and north respectively.
		+
		+	(a) Find the time when the boat is due north of its initial position.
		+
		+	b) Find an expression for the speed of the boat at time
		+	<math>t</math>.
		+
		+	c) Find the time when the boat is travelling north.
		+
		+	d) Show that the acceleration of the boat is constant and state the direction of the acceleration.
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.8a\|Answer b\|Answer 18.8b\|Answer c\|Answer 18.8c\|Answer d\|Answer 18.8d\|Solution a\|Solution 18.8a\|Solution b\|Solution 18.8b\|Solution c\|Solution 18.8c\|Solution d\|Solution 18.8d}}

Ian den 17 november 2009 kl. 14.34

Ian — Tue, 17 Nov 2009 14:34:41 GMT

← Äldre version		Versionen från 17 november 2009 kl. 14.34
Rad 156:		Rad 156:
	===Exercise 18.7===		===Exercise 18.7===
	<div class="ovning">		<div class="ovning">
		+
		+	An aeroplane moves so that at time
		+	<math>t</math>
		+	seconds, its position vectors,
		+	<math>\mathbf{r}</math>
		+	metres, is given by:
		+
		+	<math>\mathbf{r}=\left( 40t \right)\mathbf{i}+\left( 3{{t}^{2}}+20t \right)\mathbf{j}\text{ }</math>
		+
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are that are directed horizontally and vertically respectively. The aeroplane is initially at ground level.
		+
		+	a) Find the time when the height of the aeroplane is 500 metres.
		+
		+	b) Find the speed of the aeroplane at this time.
		+
		+	c) Show that the acceleration of the aeroplane is constant and state its magnitude.



	</div>{{#NAVCONTENT:Answer a\|Answer 18.7a\|Answer b\|Answer 18.7b\|Answer c\|Answer 18.7c\|Solution a\|Solution 18.7a\|Solution b\|Solution 18.7b\|Solution c\|Solution 18.7c}}		</div>{{#NAVCONTENT:Answer a\|Answer 18.7a\|Answer b\|Answer 18.7b\|Answer c\|Answer 18.7c\|Solution a\|Solution 18.7a\|Solution b\|Solution 18.7b\|Solution c\|Solution 18.7c}}

Ian den 17 november 2009 kl. 14.31

Ian — Tue, 17 Nov 2009 14:31:02 GMT

← Äldre version		Versionen från 17 november 2009 kl. 14.31
Rad 128:		Rad 128:
	===Exercise 18.6===		===Exercise 18.6===
	<div class="ovning">		<div class="ovning">
		+
		+	A particle, of mass 5 kg, moves so that its position vector,
		+	<math>\mathbf{r}</math>
		+	metres, at time
		+	<math>t</math>
		+	seconds is given by:
		+
		+	<math>\mathbf{r}=(12-2{{t}^{2}})\mathbf{i}+(10-5{{t}^{2}})\mathbf{j}</math>
		+
		+	The unit vectors <math>\mathbf{i}</math> and <math>\mathbf{j}</math> are perpendicular.
		+
		+	a) Find the position of the particle when
		+	<math>t=\text{ 1}0</math>.
		+
		+	b) Find the speed of the particle when
		+	<math>t=\text{ 2}</math>.
		+
		+	c) Find the magnitude of the resultant force on the particle when
		+	<math>t=\text{ 6}</math>.

Ian den 17 november 2009 kl. 14.25

Ian — Tue, 17 Nov 2009 14:25:50 GMT

← Äldre version		Versionen från 17 november 2009 kl. 14.25
Rad 101:		Rad 101:
	<div class="ovning">		<div class="ovning">

		+	A particle moves so that its displacement,
		+	<math>s</math>
		+	m, at time
		+	<math>t</math>
		+	seconds is given by
		+	<math>s=k{{t}^{2}}-\frac{5{{t}^{3}}}{3}</math>.

		+	a) Show that the particle is at rest when
		+	<math>t~=\text{ }0</math>.

-	</div>{{#NAVCONTENT:~~Answer a\|Answer 18.5a\|~~Answer b\|Answer 18.5b\|Answer c\|Answer 18.5c\|Answer d\|Answer 18.5d\|Solution a\|Solution 18.5a\|Solution b\|Solution 18.5b\|~~Solution~~ c\|~~Solution~~ 18.5c\|Solution d\|Solution 18.5d}}	+	b) Find k, if the particle comes to rest when
		+	<math>t~=\text{ 2}0</math>.
		+
		+	c) Sketch an acceleration-time graph for the particle.
		+
		+	d) Find the time when the acceleration of the particle is zero.
		+
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer b\|Answer 18.5b\|Answer c\|Answer 18.5c\|Answer d\|Answer 18.5d\|Solution a\|Solution 18.5a\|Solution b\|Solution 18.5b\|Hint c\|Hint 18.5c\|Solution d\|Solution 18.5d}}

Ian den 17 november 2009 kl. 14.20

Ian — Tue, 17 Nov 2009 14:20:24 GMT

← Äldre version		Versionen från 17 november 2009 kl. 14.20
Rad 97:		Rad 97:

	</div>{{#NAVCONTENT:Answer a\|Answer 18.4a\|Answer b\|Answer 18.4b\|Answer c\|Answer 18.4c\|Solution a\|Solution 18.4a\|Solution b\|Solution 18.4b\|Solution c\|Solution 18.4c}}		</div>{{#NAVCONTENT:Answer a\|Answer 18.4a\|Answer b\|Answer 18.4b\|Answer c\|Answer 18.4c\|Solution a\|Solution 18.4a\|Solution b\|Solution 18.4b\|Solution c\|Solution 18.4c}}
-
-

	===Exercise 18.5===		===Exercise 18.5===
Rad 105:		Rad 103:


-	</div>{{#NAVCONTENT:Answer a\|Answer 18.5a\|Answer b\|Answer 18.5b\|Answer c\|Answer 18.5c\|Solution a\|Solution 18.5a\|Solution b\|Solution 18.5b\|Solution c\|Solution 18.6c}}	+	</div>{{#NAVCONTENT:Answer a\|Answer 18.5a\|Answer b\|Answer 18.5b\|Answer c\|Answer 18.5c\|Answer d\|Answer 18.5d\|Solution a\|Solution 18.5a\|Solution b\|Solution 18.5b\|Solution c\|Solution 18.5c\|Solution d\|Solution 18.5d}}
		+

Ian den 17 november 2009 kl. 14.15

Ian — Tue, 17 Nov 2009 14:15:50 GMT

← Äldre version		Versionen från 17 november 2009 kl. 14.15
Rad 79:		Rad 79:
	<div class="ovning">		<div class="ovning">

		+	The distance,
		+	<math>s</math>
		+	m, travelled by a dragster at time
		+	<math>t</math>
		+	seconds is given by,
		+
		+	<math>s=36{{t}^{2}}-2{{t}^{3}}</math>
		+
		+	This expression only applies until the acceleration of the dragster becomes zero for the first time.
		+
		+	a) Find the time when the acceleration of the dragster is zero.
		+
		+	b) Find the speed of the dragster at this time.
		+
		+	c) Find the maximum acceleration of the dragster.

Ian den 17 november 2009 kl. 14.12

Ian — Tue, 17 Nov 2009 14:12:54 GMT

← Äldre version		Versionen från 17 november 2009 kl. 14.12
Rad 72:		Rad 72:

	d) Find the height of the load at this time.		d) Find the height of the load at this time.
-

	</div>{{#NAVCONTENT:Answer b\|Answer 18.3b\|Answer c\|Answer 18.3c\|Answer d\|Answer 18.3d\|Solution a\|Solution 18.3a\|Solution b\|Solution 18.3b\|Solution c\|Solution 18.3c\|Solution d\|Solution 18.3d}}		</div>{{#NAVCONTENT:Answer b\|Answer 18.3b\|Answer c\|Answer 18.3c\|Answer d\|Answer 18.3d\|Solution a\|Solution 18.3a\|Solution b\|Solution 18.3b\|Solution c\|Solution 18.3c\|Solution d\|Solution 18.3d}}
		+
		+
		+	===Exercise 18.4===
		+	<div class="ovning">
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.4a\|Answer b\|Answer 18.4b\|Answer c\|Answer 18.4c\|Solution a\|Solution 18.4a\|Solution b\|Solution 18.4b\|Solution c\|Solution 18.4c}}
		+
		+
		+
		+	===Exercise 18.5===
		+	<div class="ovning">
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.5a\|Answer b\|Answer 18.5b\|Answer c\|Answer 18.5c\|Solution a\|Solution 18.5a\|Solution b\|Solution 18.5b\|Solution c\|Solution 18.6c}}
		+
		+
		+
		+	===Exercise 18.6===
		+	<div class="ovning">
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.6a\|Answer b\|Answer 18.6b\|Answer c\|Answer 18.6c\|Solution a\|Solution 18.6a\|Solution b\|Solution 18.6b\|Solution c\|Solution 18.6c}}
		+
		+
		+
		+	===Exercise 18.7===
		+	<div class="ovning">
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.7a\|Answer b\|Answer 18.7b\|Answer c\|Answer 18.7c\|Solution a\|Solution 18.7a\|Solution b\|Solution 18.7b\|Solution c\|Solution 18.7c}}

Ian den 17 november 2009 kl. 14.08

Ian — Tue, 17 Nov 2009 14:08:28 GMT

← Äldre version		Versionen från 17 november 2009 kl. 14.08
Rad 49:		Rad 49:
	c) Find the magnitude of the resultant force on the particle at this time.		c) Find the magnitude of the resultant force on the particle at this time.

		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.2a\|Answer b\|Answer 18.2b\|Answer c\|Answer 18.2c\|Solution a\|Solution 18.2a\|Solution b\|Solution 18.2b\|Solution c\|Solution 18.2c}}


-	</div>{{#NAVCONTENT:Answer a\|Answer 18.2a\|Answer b\|Answer 18.2b\|Answer c\|Answer 18.2c\|Solution a\|Solution 18.2a\|Solution b\|Solution 18.2b\|Solution c\|Solution 18.2c}}	+	===Exercise 18.3===
		+	<div class="ovning">
		+
		+	A crane lifts a load from ground level. The height,
		+	<math>s</math>
		+	m, of the lift at time
		+	<math>t</math>
		+	seconds is given by
		+	<math>s=\frac{3{{t}^{2}}}{50}-\frac{{{t}^{3}}}{250}</math>
		+	for
		+	<math>0\le t\le 10</math>.
		+
		+	a) Show that the velocity of the load is zero when
		+	<math>t=\text{ 1}0</math>.
		+
		+	b) Find the height of the load at this time.
		+
		+	c) Find the time when the acceleration of the load is zero.
		+
		+	d) Find the height of the load at this time.
		+
		+
		+	</div>{{#NAVCONTENT:Answer b\|Answer 18.3b\|Answer c\|Answer 18.3c\|Answer d\|Answer 18.3d\|Solution a\|Solution 18.3a\|Solution b\|Solution 18.3b\|Solution c\|Solution 18.3c\|Solution d\|Solution 18.3d}}

Ian den 17 november 2009 kl. 14.03

Ian — Tue, 17 Nov 2009 14:03:12 GMT

← Äldre version		Versionen från 17 november 2009 kl. 14.03
Rad 29:		Rad 29:
	c) Find the times when the acceleration of the car is zero.		c) Find the times when the acceleration of the car is zero.

		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.1a\|Answer b\|Answer 18.1b\|Answer c\|Answer 18.1c\|Solution a\|Solution 18.1a\|Solution b\|Solution 18.1b\|Solution c\|Solution 18.1c}}


-	</div>{{#NAVCONTENT:Answer a\|Answer 18.1a\|Answer b\|Answer 18.1b\|Answer c\|Answer 18.1c\|Solution a\|Solution 18.1a\|Solution b\|Solution 18.1b\|Solution c\|Solution 18.1c}}	+
		+	===Exercise 18.2===
		+	<div class="ovning">
		+
		+	A particle, of mass 4 kg, accelerates from rest so that the distance that it has travelled in
		+	<math>t</math>
		+	seconds is
		+	<math>s</math>
		+	where
		+	<math>s=5{{t}^{2}}-6t</math>.
		+
		+	a) Find the velocity and acceleration of the particle.
		+
		+	b) Find the time when the velocity is zero.
		+
		+	c) Find the magnitude of the resultant force on the particle at this time.
		+
		+
		+
		+	</div>{{#NAVCONTENT:Answer a\|Answer 18.2a\|Answer b\|Answer 18.2b\|Answer c\|Answer 18.2c\|Solution a\|Solution 18.2a\|Solution b\|Solution 18.2b\|Solution c\|Solution 18.2c}}