Practise questions · Salam Academy

SA-9709-P3-VE-0031 markL1 FoundationCalculatorScalar product

Find

\mathbf{a}\cdot\mathbf{b}

where

\mathbf{a}=\begin{pmatrix}3\\-1\\2\end{pmatrix}

and

\mathbf{b}=\begin{pmatrix}1\\4\\-2\end{pmatrix}

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-0011 markL1 FoundationCalculatorMagnitude

Find

|3\mathbf{i}-4\mathbf{j}+12\mathbf{k}|

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-0023 marksL1 FoundationCalculatorPosition vectors

A

is

(2,-1,5)

and

B

is

(6,3,-1)

. Find the coordinates of the midpoint

M

of

AB

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE1-G013 marksL1 FoundationCalculatorMagnitude

\overrightarrow{OA}=3\mathbf{i}-\mathbf{j}+2\mathbf{k}

and

\overrightarrow{OB}=\mathbf{i}+3\mathbf{j}+2\mathbf{k}

. Find the components of

\overrightarrow{AB}

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE2-G011 markL1 FoundationCalculatorScalar product

\mathbf{a}=2\mathbf{i}+\mathbf{j}+3\mathbf{k}

and

\mathbf{b}=\mathbf{i}-4\mathbf{j}+2\mathbf{k}

. Find

\mathbf{a}\cdot\mathbf{b}

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P3-VE3-G013 marksL1 FoundationCalculatorLine equation

The line

l

has equation

\mathbf{r}=\begin{pmatrix}2\\0\\-1\end{pmatrix}+\lambda\begin{pmatrix}1\\3\\2\end{pmatrix}

. Find the coordinates of the point on

l

where

\lambda=3

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW-0011 markL1 FoundationCalculatorKE and PE

Find the kinetic energy of a car of mass

1500

kg moving at

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

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW-0021 markL1 FoundationCalculatorKE and PE

Find the gain in potential energy when a

50

kg mass is raised through

3

m.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW-0032 marksL1 FoundationCalculatorConservation of energy

A ball is dropped from rest from a height of

20

m. Ignoring air resistance, use conservation of energy to find its speed just before it hits the ground.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW-0062 marksL1 FoundationCalculatorPower

A car's engine works at

30

kW against a constant resistance of

1200

N on level ground. Find the car's maximum speed.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW-0092 marksL1 FoundationCalculatorWork

A box of mass

10

kg is pulled

8

m across a rough horizontal floor (

\mu=0.3

). Find the work done against friction.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW-0102 marksL1 FoundationCalculatorPower

A crane lifts a

200

kg load through

15

m at constant speed in

20

s. Find the average power.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW1-0011 markL1 FoundationCalculatorWork

A horizontal force of

25

N pushes a box

6

m across a floor. Find the work done by the force.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW1-0022 marksL1 FoundationCalculatorWork

A sledge is pulled

10

m across horizontal snow by a rope with tension

40

N inclined at

25^\circ

above the horizontal. Find the work done by the tension, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW1-0031 markL1 FoundationCalculatorWork against gravity

A box of mass

30

kg is lifted vertically through

4

m. Find the work done against gravity.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW2-0011 markL1 FoundationCalculatorKE and PE

Find the kinetic energy of a ball of mass

0.4

kg moving at

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

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW2-0032 marksL1 FoundationCalculatorKE and PE

A particle of mass

2

kg has kinetic energy

100

J. Find its speed.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW3-0022 marksL1 FoundationCalculatorWork–energy

A car of mass

1200

kg travelling at

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

brakes on a level road with a constant braking force of

7500

N. Use the work–energy principle to find its stopping distance.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW4-0011 markL1 FoundationCalculatorPower

A car's driving force is

2000

N when it is moving at

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

. Find the power of its engine, in kW.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P4-EW4-0022 marksL1 FoundationCalculatorPower

A motor lifts a load of mass

500

kg through a vertical height of

12

m at constant speed in

30

s. Find the power of the motor.

Salam Academy Original Practice · Proposed mark scheme

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