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Kinematics
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Computations involving distance, displacement, velocity, and acceleration
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Displacement vs Distance
SL 5.9
Displacement s is the change in position between start and end time, whereas distance d is the total length of the path taken.
Direction does not matter for distance, which is never negative, but displacement can be negative - usually indicating motion down or to the left.
Displacement, velocity and acceleration
SL 5.9
Acceleration is the rate of change of velocity, which is the rate of change of displacement.
v=dtds🚫\\
a=dtdv=dt2d2s📖
Hence, the integral of acceleration is velocity, and the integral of velocity is displacement.
Average Velocity and Acceleration
SL 5.9
While we use derivatives to get instantaneous velocity and time, we can also find average velocity and time:
average velocity=ΔtΔs,average acceleration=ΔtΔv.
Change in Displacement from Velocity
SL 5.9
Change in displacement between t1,t2:
∫t1t2v(t)dt📖
Speed
SL 5.9
Speed is the magnitude of velocity:
speed=∣v∣
Distance from Velocity
SL 5.9
The distance can be found from the velocity using the equation
∫t1t2∣v(t)∣dt📖
Since speed is given by ∣v(t)∣, we see that distance is the integral of speed.
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