Units and Kinematics Chapter 7
Variable acceleration
s.u.v.a.t
s = displacement (m)
u = initial velocity (ms-1)
v = velocity (ms-1)
a = acceleration (ms-2)
t = time (sec)
5 KEY SUVAT EQUATIONS
1) v = u+at
2) v2 = u2+2as
3) s = 1/2 (u+v) t
4) s vt - 1/2 at2
5) s = ut + 1/2 at2
TERMS TO DESCRIBE LOCATION AND MOVEMENT
postition is a vector: the distance and direction from the origin
Displacement is a vector: the change of position
Distance is a scalar: the magnitude of displacement
Velocity is a vector: the rate of change of displacement
Speed is a scalar: the magnitude of velocity.
Displacement-time graphs
The gradient of the graph is the velocity
Gradient = change in displacement / change in time
Average velocity = resultant displacement / total time
Average speed = total distance / total time
Velocity-time graphs
gradient = rate of change of velocity = acceleration
Acceleration = change in velocity / time
The area between the velocity-time graph and the time axis is the displacement
Negative acceleration is sometimes called deceleration, though it often means slowing down, the acceleration can be negative but the speed can still be increasing.
The gradient of a tangent to a non linear displacement-time graph = the acceleration at that instant
If you know the displacement as a function of time, you can work out the gradient (velocity) by differentiation. (the rate of change of displacement).
v = ds/dt
Similarly, acceleration is the rate of change of velocity so you can obtain acceleration by differentiation velocity with respect to time (double differentiation of displacement)
a = dv/dt = d2s/dt2
You can also do this in reverse by integrating
s = ∫ vdt and v = ∫ adt