Practise questions · Salam Academy

SA-9709-P4-KM4-0013 marksL1 FoundationCalculatorCalculus

A particle has displacement

s=t^3-3t^2+5

m at time

t

s. Find its velocity and its acceleration when

t=2

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM4-0081 markL1 FoundationCalculatorDistance with turning

To find when a particle changes direction, you should solve

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM-Q031 markL1 FoundationCalculatorCalculus

If

s

is displacement, velocity is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM-0065 marksL2 StandardCalculatorCalculus

A particle moves in a straight line with velocity

v=3t^2-12t+9\ \text{m s}^{-1}

. Find the times when it is at rest, its acceleration when

t=4

, and its displacement from its starting point at

t=1

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM-0083 marksL2 StandardCalculatorCalculus

A particle starts from rest with acceleration

a=6-2t\ \text{m s}^{-2}

. Find its greatest velocity.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM4-0024 marksL2 StandardCalculatorCalculus

A particle starts from rest at

O

and moves with acceleration

a=4t\ \text{m s}^{-2}

. Find its velocity and its displacement from

O

when

t=3

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM4-0053 marksL2 StandardCalculatorCalculus

A particle moves with velocity

v=2t^2-8t+10\ \text{m s}^{-1}

. Find the time at which its velocity is least, and the least velocity.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM4-0063 marksL2 StandardCalculatorCalculus

A particle moves with velocity

v=3t^2-2t+1\ \text{m s}^{-1}

. When

t=0

it is

4

m from

O

on the positive side. Find its displacement from

O

when

t=2

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM-0074 marksL3 ExamCalculatorDistance with turning

For the particle with

v=3t^2-12t+9

, find the total distance travelled from

t=0

to

t=3

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM4-0035 marksL3 ExamCalculatorDistance with turning

A particle leaves

O

with velocity

v=8t-2t^2\ \text{m s}^{-1}

. Find its greatest displacement from

O

in the positive direction, and the time when it returns to

O

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM4-0045 marksL3 ExamCalculatorDistance with turning

A particle moves with velocity

v=t^2-4t+3\ \text{m s}^{-1}

. Find the total distance travelled from

t=0

to

t=4

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM4-0074 marksL3 ExamCalculatorCalculus

A particle starts from rest with acceleration

a=12-6t\ \text{m s}^{-2}

. Find the time when it is next at rest, and the distance it has travelled by then.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM4-0094 marksL3 ExamCalculatorCalculus

For

0\le t\le2

a particle has velocity

v=3t^2\ \text{m s}^{-1}

; for

t>2

it moves at a constant

12\ \text{m s}^{-1}

. Find the distance travelled in the first

5

s.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-KM-0136 marksL4 ChallengingCalculatorDistance with turning

A particle moves with

v=t^2-8t+12\ \text{m s}^{-1}

. Find the total distance travelled from

t=0

to

t=6

.

Salam Academy Original Practice · Proposed mark scheme

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