In Fig. 2.17, the object negatively accelerates (slows down) to rest with non-uniform acceleration.
Time (s) FIG. 2.17
General conclusions From both sets of graphs you can see:
• Identical slopes indicate the same velocity or acceleration. • A horizontal line means that the y value is constant and unchanging. • A negative slope in velocity–time graphs means negative acceleration. • The area under a velocity–time graph is equal to distance travelled.
Measuring velocity and acceleration
Ticker timer and tape As with measurements of velocity, a ticker timer and tape can be used to record acceleration. Acceleration is the change in velocity as time passes. So you will have a piece of tape similar to the one in Fig. 2.18.
• The final velocity can be found by dividing the distance CD at the end of the tape from C to D by 2
___ 50 = 0.04 second.
___ 50 = 0.04 second.
Now you need to put the results into the formula for acceleration: a = v – u Calculation: Distance |AB| = 3.9 cm. Therefore u = 3.9 × 10–2 m = 0.975 m s–1
___ 50 = 0.16 second.
______ t .
Distance |CD| = 1.1 cm. Therefore v = 1.1 × 10–2 m = 0.275 m s–1
_______________ 0.04 s
_______________ 0.04 s
Therefore, a = 0.275 – 0.975 = –4.375 m s–2
________________ 0.16
18 FUSION
To find the acceleration you now need to work out how much time passed from the initial velocity u to the final velocity v. This is the number of spaces between the middle of each velocity. In Fig. 2.18, this is 8 spaces, so the time t is 8
Middle velocity
Middle velocity
AB C FIG. 2.18 The pattern on a ticker timer tape measuring velocity
• The physical displacements can be measured with a metre rule from point A to point B and from point C to point D.
• The initial velocity u can be found from A to B in the same way as before, by dividing the distance |AB| by 2
