Using the SUVAT Equations | CAIE 9702 Paper 2 Notes

Paper 2

Physics9702

Using the SUVAT Equations

Do not select an equation from the wording alone. First confirm that acceleration is constant and the motion can be treated along one straight line. Then translate the information into

u,v,a,s,t

The method

Write u, v, a, s, t and fill in the three values or conditions the question gives. Convert words such as “starts from rest” into $u=0$ .
Mark the one you want.
Identify the quantity that is neither known nor required. Choose the relation that leaves out that quantity, substitute and solve.
Check the unit, direction and physical size of the result. A negative answer may indicate direction rather than an error.

Before you start, choose one and give every vector a sign that matches it. If up is positive, then $g = -9.81 \text{ m s}^{-2}$ ; if down is positive, $g = +9.81 \text{ m s}^{-2}$ .

Choose one positive direction and give every vector a sign that matches it. Both choices work; mixing them in one calculation is what loses the marks.

Worked example

Warm-up: a dropped ball

A ball is dropped from rest and falls 5.0 m. Find its speed just before it lands.

A hand releasing a small ball that falls toward the ground. — Dropped from rest, the ball speeds up over the 5.0 m fall under gravity alone.

Take down as positive: $u = 0,\; s = 5.0 \text{ m},\; a = 9.81 \text{ m s}^{-2}$ ; we want $v$ .
The missing letter is $t$ , so use $v^2 = u^2 + 2as$ .
$v^2 = 0 + 2 \times 9.81 \times 5.0 = 98.1$ , so $v = 9.9 \text{ m s}^{-1}$ .

Answer

v = 9.9 \text{ m s}^{-1}

Worked example

A harder step: thrown straight up

A ball is thrown straight up at 20 m s⁻¹. Find the greatest height it reaches.

The fact to notice: at the very top the ball is still for an instant, so $v = 0$ .
Take up as positive: $u = +20$ , $a = -9.81 \text{ m s}^{-2}$ ; we want $s$ . The missing letter is $t$ , so use $v^2 = u^2 + 2as$ :
$0 = 20^2 + 2(-9.81)s$
$s = \dfrac{400}{19.62} = 20.4 \approx 20 \text{ m}$ .

Answer

s \approx 20 \text{ m}

Your turnquick check

A question gives u, v, a and s, but no time. Which SUVAT equation should you choose?

Show worked answer

Use $v^2=u^2+2as$ , because it is the equation that leaves out t.

Using the SUVAT Equations

Do not select an equation from the wording alone. First confirm that acceleration is constant and the motion can be treated along one straight line. Then translate the information into

u,v,a,s,t

The method

Write u, v, a, s, t and fill in the three values or conditions the question gives. Convert words such as “starts from rest” into $u=0$ .
Mark the one you want.
Identify the quantity that is neither known nor required. Choose the relation that leaves out that quantity, substitute and solve.
Check the unit, direction and physical size of the result. A negative answer may indicate direction rather than an error.

Before you start, choose one and give every vector a sign that matches it. If up is positive, then $g = -9.81 \text{ m s}^{-2}$ ; if down is positive, $g = +9.81 \text{ m s}^{-2}$ .

Choose one positive direction and give every vector a sign that matches it. Both choices work; mixing them in one calculation is what loses the marks.

Worked example

Warm-up: a dropped ball

A ball is dropped from rest and falls 5.0 m. Find its speed just before it lands.

Take down as positive: $u = 0,\; s = 5.0 \text{ m},\; a = 9.81 \text{ m s}^{-2}$ ; we want $v$ .
The missing letter is $t$ , so use $v^2 = u^2 + 2as$ .
$v^2 = 0 + 2 \times 9.81 \times 5.0 = 98.1$ , so $v = 9.9 \text{ m s}^{-1}$ .

Answer

v = 9.9 \text{ m s}^{-1}

Worked example

A harder step: thrown straight up

A ball is thrown straight up at 20 m s⁻¹. Find the greatest height it reaches.

The fact to notice: at the very top the ball is still for an instant, so $v = 0$ .
Take up as positive: $u = +20$ , $a = -9.81 \text{ m s}^{-2}$ ; we want $s$ . The missing letter is $t$ , so use $v^2 = u^2 + 2as$ :
$0 = 20^2 + 2(-9.81)s$
$s = \dfrac{400}{19.62} = 20.4 \approx 20 \text{ m}$ .

Answer

s \approx 20 \text{ m}

Your turnquick check

A question gives u, v, a and s, but no time. Which SUVAT equation should you choose?

Show worked answer

Use $v^2=u^2+2as$ , because it is the equation that leaves out t.