Displacement, distance, velocity and acceleration in one and two dimensions, including v=dtds,
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.
Acceleration is the rate of change of velocity, which is the rate of change of displacement.
Hence, the integral of acceleration is velocity, and the integral of velocity is displacement.
While we use derivatives to get instantaneous velocity and time, we can also find average velocity and time:
Change in displacement between t1,t2:
Speed is the magnitude of velocity:
If the velocity and acceleration of an object point in the same direction, we say the object is "speeding up" since its speed increases.
If the velocity and acceleration of an object point in opposite directions, we instead say the object is "slowing down."
The distance can be found from the velocity using the equation
Since speed is given by ∣v(t)∣, we see that distance is the integral of speed.
We can extend these kinematics concepts to two dimensions using vectors.
For example, the velocity vector v=(32t−1) represents a constant velocity of 3 in the x direction, and a variable velocity vy(t)=2t−1 in the y-direction.
The speed of the object is just the magnitude of the velocity:
Nice work completing Kinematics, here's a quick recap of what we covered:
Exercises checked off
Displacement, distance, velocity and acceleration in one and two dimensions, including v=dtds,
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.
Acceleration is the rate of change of velocity, which is the rate of change of displacement.
Hence, the integral of acceleration is velocity, and the integral of velocity is displacement.
While we use derivatives to get instantaneous velocity and time, we can also find average velocity and time:
Change in displacement between t1,t2:
Speed is the magnitude of velocity:
If the velocity and acceleration of an object point in the same direction, we say the object is "speeding up" since its speed increases.
If the velocity and acceleration of an object point in opposite directions, we instead say the object is "slowing down."
The distance can be found from the velocity using the equation
Since speed is given by ∣v(t)∣, we see that distance is the integral of speed.
We can extend these kinematics concepts to two dimensions using vectors.
For example, the velocity vector v=(32t−1) represents a constant velocity of 3 in the x direction, and a variable velocity vy(t)=2t−1 in the y-direction.
The speed of the object is just the magnitude of the velocity:
Nice work completing Kinematics, here's a quick recap of what we covered:
Exercises checked off