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. Explain why A + 2 B = 40

According to the given values of s for different ranges of time, s is continuous at t = 4 . The value of distance can be calculated in two given ranges. Hence: The distance fell by the parachute in 4 s : A 4 + 4 B = 5 × 16 ⇒ 2 A + 4 B = 80 ⇒ A + 2 B = 40 Hence shown.

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.

EASY

AS and A Level

IMPORTANT

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A tennis ball is projected vertically upwards. The vertical displacement of the ball, in metres, from the point of projection at time $t$ seconds is given by $s = - 5 t^{2} + 8 t$
Find the time when the ball returns to its starting point.

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 6

A tennis ball is projected vertically upwards. The vertical displacement of the ball, in metres, from the point of projection at time

t

seconds is given by

s = - 5 t^{2} + 8 t

Find the displacement when the ball is momentarily 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 6A>Q 8

In a drag race, two cars,

A

and

B

, line up side by side at the start point. When the starting flag is waved, both cars are driven as fast as possible in a straight line. The first car to cross the finish line is the winning car. At time

t s

from when the cars start to move, the distance travelled by car

A

is given by

s = 4 t + t^{2} .

Car A takes

16 s

to reach the finish line.
Work out the distance from the start to the finish.

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 8

In a drag race, two cars,

A

and

B

t s

from when the cars start to move, the distance travelled by car

A

is given by

s = 4 t + t^{2} .

Car A takes

16 s

to reach the finish line. Find the speed of car

A

when it crosses the finish 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 8

In a drag race, two cars,

A

and

B

t s

from when the cars start to move, the distance travelled by car

A

is given by

s = 4 t + t^{2} .

Car A takes

16 s

to reach the finish line. At time

t

s from when the cars start to move, the distance travelled by car

B

is given by

s = 1.2 t^{2}

. Find the speed of car

B

when it crosses the finish 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 8

In a drag race, two cars,

A

and

B

t s

from when the cars start to move, the distance travelled by car

A

is given by

s = 4 t + t^{2} .

Car A takes

16 s

to reach the finish line. At time

t

s from when the cars start to move, the distance travelled by car

B

is given by

s = 1.2 t^{2}

. When the winning car crosses the finish line, how far behind it is the other car?

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 9

A burglar moves along a straight corridor from one door to the next door. At time

t s

his distance,

s m

, from the door of the first room is given by

s = 1.8 t^{2} - 0.3 t^{4} .

He starts and finishes with speed

v = 0 m s^{- 1}

. Find the distance between the two doors.

EASY

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. Explain why

A + 2 B = 40

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. 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

A tennis ball is projected vertically upwards. The vertical displacement of the ball, in metres, from the point of projection at time t seconds is given by s=-5t2+8t Find the time when the ball returns to its starting point.

Important Questions on General Motion in a Straight Line

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A tennis ball is projected vertically upwards. The vertical displacement of the ball, in metres, from the point of projection at time $t$ seconds is given by $s = - 5 t^{2} + 8 t$
Find the time when the ball returns to its starting point.