At time t s after jumping from a plane, the distance fallen by a parachutist is modelled as s m , where s = 5 t 2 : 0 ⩽ t ⩽ 4 A t + B t : 4 < t ⩽ 25 C t + 30 : 25 < t ⩽ 50 A , B and C are constants. The parachute is opened at t = 4 and the speed of the parachutist is immediately reduced by x m s - 1 . Show that 0 . 25 A + B = 40 - x

The speed of parachute at t = 4 s : d d t 5 t 2 = 10 t = 10 × 4 = 40 m s - 1 ......(i) The speed of parachute immediately after t = 4 s : d d t A t + B t = A 2 × 1 t + B = A 2 × 1 2 + B = 0 . 25 A + B m s - 1 .....(ii) (ii) is less than (i) by x m s - 1 . Hence, we can write: 0 . 25 A + B = 40 - x .....(iii) (iii) is the rquired expression.

At time t s after jumping from a plane, the distance fallen by a parachutist is modelled as s m , where s = 5 t 2 : 0 ⩽ t ⩽ 4 A t + B t : 4 < t ⩽ 25 C t + 30 : 25 < t ⩽ 50 A , B and C are constants. The parachute is opened at t = 4 and the speed of the parachutist is immediately reduced by x m s - 1 . Show that 0 . 25 A + B = 40 - x

The speed of parachute at t = 4 s : d d t 5 t 2 = 10 t = 10 × 4 = 40 m s - 1 ......(i) The speed of parachute immediately after t = 4 s : d d t A t + B t = A 2 × 1 t + B = A 2 × 1 2 + B = 0 . 25 A + B m s - 1 .....(ii) (ii) is less than (i) by x m s - 1 . Hence, we can write: 0 . 25 A + B = 40 - x .....(iii) (iii) is the rquired expression.

At time t s after jumping from a plane, the distance fallen by a parachutist is modelled as s m , where s = 5 t 2 : 0 ⩽ t ⩽ 4 A t + B t : 4 < t ⩽ 25 C t + 30 : 25 < t ⩽ 50 A , B and C are constants. At t = 25 the speed of the parachute becomes constant. Write down two equations that connect A , B and C .

The distance covered at t = 25 is given by: s = A t + B t = A 25 + 25 B = 5 A + 25 B .....(i) The distance covered just after this = C t + 30 = 25 C + 30 .....(ii) s is continuous at t = 25 . Hence, (i) and (ii) are equal. 5 A + 25 B = 25 C + 30 ⇒ A + 5 B = 5 C + 6 ......(iii) The speed of the parachute becomes constant at t = 25 hence: d d t A t + B t = d d t C t + 30 ⇒ A 2 × 1 t + B = C ⇒ A 10 + B = C ⇒ A + 10 B = 10 C ........(iv) (iii) and (iv) are the required equations.

MEDIUM

AS and A Level

IMPORTANT

Earn 100

At time $t$ s after jumping from a plane, the distance fallen by a parachutist is modelled as $s m$ , where
$s = \{\begin{cases} 5 t^{2} : 0 ⩽ t ⩽ 4 \\ A \sqrt{t} + B t : 4 < t ⩽ 25 \\ C t + 30 : 25 < t ⩽ 50 \end{cases}$
$A, B$ and $C$ are constants. The parachute is opened at $t = 4$ and the speed of the parachutist is immediately reduced by $x m s^{- 1}$ . Show that $0.25 A + B = 40 - x$

Important Questions on General Motion in a Straight Line

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6A>Q 10

At time

t

s after jumping from a plane, the distance fallen by a parachutist is modelled as

s m

, where

s = \{\begin{cases} 5 t^{2} : 0 ⩽ t ⩽ 4 \\ A \sqrt{t} + B t : 4 < t ⩽ 25 \\ C t + 30 : 25 < t ⩽ 50 \end{cases}

A, B

and

C

are constants. At

t = 25

the speed of the parachute becomes constant. Write down two equations that connect

A, B

and

C .

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6A>Q 10

At time

t

s after jumping from a plane, the distance fallen by a parachutist is modeled as

s m

, where

s = \{\begin{cases} 5 t^{2} : 0 ⩽ t ⩽ 4 \\ A \sqrt{t} + B t : 4 < t ⩽ 25 \\ C t + 30 : 25 < t ⩽ 50 \end{cases}

Where

A, B

and

C

are constants. The parachute is opened at

t = 4

and the speed of the parachutist is immediately reduced by

x m s^{- 1}

. At

t = 25

the speed of the parachute becomes constant. Find the value of

x .

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6A>Q 11

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

s m

, from its initial position

O

is given by

s = - 0.6 t^{4} + 2.4 t^{3} - 3.6 t^{2} + 2.4 t

for

0 < t < 4

, where

t s

is the time for which the particle has been travelling.
Show that the particle starts moving along the line in the positive direction.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6A>Q 11

A particle moves forwards and backward along a straight line. The displacement of the particle,

s m

, from its initial position

O

is given by

s = - 0.6 t^{4} + 2.4 t^{3} - 3.6 t^{2} + 2.4 t

for

0 < t < 4

, where

t s

is the time for which the particle has been travelling. The particle comes to instantaneous rest at point

A

, returns to pass through

O

and continues to point

B

, where the distance

O B

is the same as the distance

O A .

Find the speed of the particle when it is at

B

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6A>Q 12

A robot moves along a straight line for

10 s

. The displacement of the robot,

s m

, from its initial position is given by

s = - 0.01 t^{4} + 0.2 t^{3} - 1.32 t^{2} + 3.2 t

, where

t

is measured in seconds and

0 < t < 10 .

Show that the robot is stationary when

t = 2, t = 5

and

t = 8 .

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 6 - General Motion in a Straight Line>EXERCISE 6A>Q 12

A robot moves along a straight line for

10 s

. The displacement of the robot,

s m

, from its initial position is given by

s = - 0.01 t^{4} + 0.2 t^{3} - 1.32 t^{2} + 3.2 t

, where

t

is measured in seconds and

0 < t < 10 .

The robot is stationary when

t = 2, t = 5

and

t = 8 .

Find the distance that the robot travels in the

10 s

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 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 time when the particle is stationary.

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 2

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

v m s^{- 1}

, at time

t s

is given by

v = t^{3} + 3 t^{2} - 8 t + l

. Find its acceleration when

t = 2 .

At time t s after jumping from a plane, the distance fallen by a parachutist is modelled as s m, where s=5t2 :0⩽t⩽4At+Bt :4<t⩽25Ct+30 :25<t⩽50 A, B and C are constants. The parachute is opened at t=4 and the speed of the parachutist is immediately reduced by x m s-1. Show that 0.25 A+B=40-x

Important Questions on General Motion in a Straight Line

Learn and Prepare for any exam you want !