A boy runs in a straight line. The velocity of the boy, v ms - 1 , at time t s is given by: v = 2 + 3 t : 0 ⩽ t ⩽ 1 6 - t 2 : 1 ⩽ t ⩽ 1 . 2 5 - k 30 t : 1 . 2 ⩽ t ⩽ T for 0 ⩽ t ⩽ T The boy has velocity 0 m s - 1 at time T . Work out the average acceleration of the boy over the period 0 - T . Given that k = 11 and T = 13 . 6 s .

The average acceleration is calculated as the ratio of change in velocity to the interval of time in which this change has taken place. The average acceleration: a a v e r a g e = v f - v i time interval For t = 0 s , v i = 2 m s - 1 For t = 13 . 6 s , v f = 5 - 11 × 13 . 6 30 = 1 75 m s - 1 ⇒ a a v e r a g e = 1 75 - 2 13 . 6 = - 10 . 95 75 m s - 2

A boy runs in a straight line. The velocity of the boy, v ms - 1 , at time t s is given by: v = 2 + 3 t : 0 ⩽ t ⩽ 1 6 - t 2 : 1 ⩽ t ⩽ 1 . 2 5 - k 30 t : 1 . 2 ⩽ t ⩽ T for 0 ⩽ t ⩽ T The boy has velocity 0 m s - 1 at time T . Work out the average acceleration of the boy over the period 0 - T . Given that k = 11 and T = 13 . 6 s .

The average acceleration is calculated as the ratio of change in velocity to the interval of time in which this change has taken place. The average acceleration: a a v e r a g e = v f - v i time interval For t = 0 s , v i = 2 m s - 1 For t = 13 . 6 s , v f = 5 - 11 × 13 . 6 30 = 1 75 m s - 1 ⇒ a a v e r a g e = 1 75 - 2 13 . 6 = - 10 . 95 75 m s - 2

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A boy runs in a straight line. The velocity of the boy, $v {ms}^{- 1}$ , at time $t s$ is given by:
$v = \{\begin{matrix} 2 + 3 t : 0 ⩽ t ⩽ 1 \\ 6 - t^{2} : 1 ⩽ t ⩽ 1.2 \\ 5 - \frac{k}{30} t : 1.2 ⩽ t ⩽ T \end{matrix}$ for $0 ⩽ t ⩽ T$
The boy has velocity $0 m s^{- 1}$ at time $T$ . Work out the average acceleration of the boy over the period $0 - T$ . Given that $k = 11 and T = 13.6 s$ .

Important Questions on General Motion in a Straight Line

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6B>Q 5

A boy runs in a straight line. The velocity of the boy,

v {ms}^{- 1}

, at time

t s

is given by:

v = \{\begin{matrix} 2 + 3 t : 0 ⩽ t ⩽ 1 \\ 6 - t^{2} : 1 ⩽ t ⩽ 1.2 \\ 5 - \frac{k}{30} t : 1.2 ⩽ t ⩽ T \end{matrix}

for

0 ⩽ t ⩽ T

The boy has velocity

0 m s^{- 1}

at time

T

. The value for average acceleration is

13.6 m s^{- 2}

and

k = 11

. Show that there is no time at which the acceleration of the boy is the same as his average acceleration.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6B>Q 6

The motion of a cat, moving along a straight line, is modelled as

s = 6 t - t^{2}

for small values of

t,

where

s

is measured in metres and

t

in seconds.
Find an expression for the velocity of the cat as a function of time.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6B>Q 6

The motion of a cat, moving along a straight line, is modelled as

s = 6 t - t^{2}

for small values of

t,

where

s

is measured in metres and

t

in seconds.
Describe the motion of the cat.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6B>Q 6

The motion of a cat, moving along a straight line, is modelled as

s = 6 t - t^{2}

for small values of

t,

where

s

is measured in metres and

t

in seconds.
When does the cat come to momentary rest?

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6B>Q 6

The motion of a cat, moving along a straight line, is modelled as

s = 6 t - t^{2}

for small values of

t,

where

s

is measured in metres and

t

in seconds.
Find the acceleration of the cat.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6B>Q 7

A particle moves forwards and backwards along a straight line. The velocity of the particle,

v m s^{- 1}

, at time

t

s is given by

v = - t^{3} + 75 t

for

0 < t < 10

. Find the maximum speed of the particle.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6B>Q 8

A robot moves along a straight line for

3 s

. The displacement of the robot,

s m

, from its initial position is given by

s = A t^{3} + B t^{2} + C t

for constants

A, B

and

C,

where

t

is measured in seconds and

0 < t < 3

. The robot starts with velocity

2 m s^{- 1}

. It travels

6 m

before coming to rest at time

t = 3 .

Work out the values of

A, B

and

C .

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6C>Q 1

A particle moves in a straight line so that its velocity,

v m s^{- 1}

, at time

t s

(t > 0)

is given by

v = 5 t^{2} - 20

. Find the displacement of the particle when it is stationary.

A boy runs in a straight line. The velocity of the boy, v ms-1, at time t s is given by: v=2+3t:0⩽t⩽16-t2:1⩽t⩽1.25-k30t:1.2⩽t⩽T for 0⩽t⩽T The boy has velocity 0 m s-1 at time T. Work out the average acceleration of the boy over the period 0-T. Given that k=11 and T=13.6 s.

Important Questions on General Motion in a Straight Line

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