20,345
edits
Changes
no edit summary
====Using a, v, u and t====
{| class="wikitable"
| style="height:20px; width:300px; text-align:center;" |A cyclist travels at an initial velocity of 5m/s. They then take 20 seconds to increase velocity to 15m/s. Calculate the acceleration of the cyclist correct to two [[Significant Figures|significant figures]].
| style="height:20px; width:300px; text-align:center;" |A driverless car travelling at 35m/s notices a pedestrian walk into the road and begins automatic breaking. It comes to a complete stop. The acceleration is -14m/s. Calculate the time taken to come to a stop correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
u = 5m/s
v = 15m/s
t = 20s
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
a = -14m/s/s
u = 35m/s
v = 0m/s
|-
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>a=\frac{v-u}{t}</math>
<math>a=\frac{15-5}{20}</math>
<math>a=\frac{10}{20}</math>
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>a=\frac{v-u}{t}</math>
<math>-14=\frac{0-35}{t}</math>
<math>-14=\frac{-35}{t}</math>
|-
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>a=0.50m/s/s</math>
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>-14t=-35</math>
<math>t=\frac{-35}{-14}</math>
<math>t = 2.5s</math>
|}
{| class="wikitable"
| style="height:20px; width:300px; text-align:center;" |A person runs onto a thick sheet of ice. They begin to slide along. They decelerate at a rate of 0.2m/s/s for 30 seconds until they come to rest. Calculate the initial velocity of person correct to two [[Significant Figures|significant figures]].
| style="height:20px; width:300px; text-align:center;" |A safety car is out on the track with F1 cars limited to 15m/s until it pulls over. A car then accelerates at 9m/s/s for 8 seconds. Calculate the final velocity of the car correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
a = -0.2m/s/s
v = 0m/s
t = 30s
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
a = 9m/s/s
u = 15m/s
t = 8s
|-
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>a=\frac{v-u}{t}</math>
<math>-0.2=\frac{0-u}{30}</math>
<math>-0.2=\frac{-u}{30}</math>
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>a=\frac{v-u}{t}</math>
<math>9=\frac{v-15}{8}</math>
|-
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>-0.2=\frac{-u}{30}</math>
<math>-u= (-0.2) \times 30</math>
<math>u= 6.0m/s</math>
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>9 \times 8 =v-15</math>
<math>9 \times 8 + 15 = v</math>
<math>v =87m/s</math>
|}
====Using v, u a and s====
{| class="wikitable"
| style="height:20px; width:300px; text-align:center;" |A fighter jet [[accelerate]]s at 60m/s/s from rest along a runway which is 150m in length. Calculate the [[velocity]] reached by the fighter jet, correct to two [[Significant Figures|significant figures]].
| style="height:20px; width:300px; text-align:center;" |A train applies the breaks over 25m of track slowing at a rate of 0.5m/s/s to a [[velocity]] of 10m/s. Calculate the initial [[velocity]] of the train prior to breaking, correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
u = 0m/s
a = 60m/s/s
s = 150m
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
v = 10m/s
a = -0.5m/s/s
s = 25m
|-
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>v^2=u^2 + 2as</math>
<math>v^2=0^2 + 2 \times 60 \times 150</math>
<math>v^2=18000</math>
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>v^2=u^2 + 2as</math>
<math>10^2=u^2 + 2 \times (-0.5) \times 25</math>
<math>100=u^2 - 25</math>
|-
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>v=\sqrt{18000}</math>
<math>v=134.16m/s</math>
<math>v \approx 130m/s </math>
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>u^2 = 100 + 25</math>
<math>u^2 = 125</math>
<math>u=\sqrt{125}</math>
<math>u=11.18m/s</math>
<math>u \approx 11m/s</math>
|}
{| class="wikitable"
| style="height:20px; width:300px; text-align:center;" |A car travelling at 30m/s has a stopping distance of 55m. Calculate the [[deceleration]] of the car correct to two [[Significant Figures|significant figures]].
| style="height:20px; width:300px; text-align:center;" |A formula 1 car is travelling at 50m/s on a straight but must slow to 22m/s for an approaching corner. The breaks can [[decelerate]] the car at 30m/s/s. Calculate how far before the corner the car must begin braking, correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
v = 0m/s
u = 30m/s
s = 55m
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
v = 22m/s
u = 50m/s
a = -30m/s/s
|-
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>v^2=u^2 + 2as</math>
<math>0^2=30^2 + 2 \times a \times 55</math>
<math>0=900+110a</math>
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>v^2=u^2 + 2as</math>
<math>22^2=50^2 + 2 \times (-30) \times s</math>
<math>484=2500 - 60s</math>
|-
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>110a = -900</math>
<math>a =\frac{-900}{110}</math>
<math>a =\frac{-900}{110}</math>
<math>a=-8.1818m/s/s</math>
<math>a \approx -8.2m/s/s </math>
Deceleration = + 8.2m/s/s
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>484=2500 - 60s</math>
<math>60s = 2500-484</math>
<math>s =\frac{2016}{60}</math>
<math>s=33.6m</math>
<math>s \approx 34m</math>
|}