Lesson 7 — 4.4 acceleration & speed time graphs

• Natuurkunde / Scheikunde
• Middelbare school
• havo, vwo
• Leerjaar 2

This lesson

• rearranging the formula for acceleration
• speed-time graphs
  
• 
  

Learning goals 4.4

• Calculate acceleration
  
• Define the unit for acceleration
  
• Rearrange the formula for acceleration
  
• Read a speed-time graph correctly
  
• Explain terminal velocity
  

Learning goals 4.4

• Calculate acceleration
  
• Define the unit for acceleration
  
• Rearrange the formula for acceleration
  
• Read a speed-time graph correctly
  
• Explain terminal velocity
  

Recap

• What is the formula for acceleration
  
• What is the unit of acceleration. Explain your answer
  

acceleration=​time​​finalspeed−startingspeed​​

a=​t​​v​f​​−v​i​​​​

acceleration=​time​​finalspeed−startingspeed​​

Or 

a= 

Δv

÷t

a=​t​​v​f​​−v​i​​​​

acceleration=​time​​finalspeed−startingspeed​​

• a: acceleration
  
• vf: final speed
  
• vi: initial speed
  
• t: time
  

Unit of Acceleration

• speed/time
  
• (m/s)/s
  

Unit of Acceleration

• speed/time
  
• (m/s)/s
  

m/s

2

Rearranging the formula for speed

a=​t​​v​f​​−v​i​​​​

3=​2​​6​​

                                     is the same as                v = a.t 

 

                                     is the same as          

Δ

a=Δ​t​​v​​

(vf−vi)=a⋅t

t=​a​​(vf−vi)​​

t=Δ​a​​v​​

Speed-time graphs

Speed-time graphs

The area under the curve = De travelled distance. 

Speed-time graphs

area A=12   Area B=30  Area C= 9

              

         d= 51 m

The area under the graph

The area under the graph

Area under graph = 64

          d=64 m

Terminal velocity

Constant speed. travelling the same distance each second. Constant slope

(x,t)-diagram

(v,t)-diagram

Constant speed. travelling the same distance each second. Constant slope

Deccelerating (slowing down) travelling lesser distance each second. Graph is becoming less steep=. Slope is decreasing

(x,t)-diagram

(v,t)-diagram

Accelerating ( speeding up). Travelling more distance each second. Graph is becoming more steep = slope is increasing.

(x,t)-diagram

(v,t)-diagram

Exercise

Mike goes for a run. At the start of his run he runs at a speed of 7 m/s. 25 seconds later he runs at a speed of 4 m/s. Calculate his acceleration. Answer  

• Elevators in in the Yokohama tower in Japan are among the fastest in the world. They accelerate upwards at a rate of 3.125 m/s2 for 4 seconds. Starting from rest, what is their final speed? Vf= 12,5 m/s

• A cyclists cycles at a speed of 5/ms. He accelerates at a rate of 1.26 m/s² for 6.3 seconds. Calculate his final speed. vf= 12,94 m/s
  

Learning goals 4.4

• Calculate acceleration
  
• Define the unit for acceleration
  
• Rearrange the formula for acceleration
  
• Read a speed-time graph correctly
  
• Explain terminal velocity