1
Q
what is the displacement, s, of a particle?
A
the length and direction from the origin to the particle.
2
Q
calculus formulas for velocity
A
v=ds/dt v=∫adt
3
Q
calculus formulas for acceleration
A
a=dv/dt=d^2s/dt^2
4
Q
calculus formula for displacement
A
s=∫vdt
5
Q
what does gradient represent on a velocity-time and displacement-time graph?
A
instantaneous rate of change (of velocity/acceleration)
6
Q
how to find the area under a graph (with limits)
A
integration
7
Q
how to derive v=u+at
A
a=d^2s/dt^2 integrate with respect to time ∫adt=∫d^2s/dt^2 dt integrate both sides at+k=ds/dt when t=0, ds/dt=u so k=u when t=t ds/dt=v at+u=v v=u+at
8
Q
how to derive s=ut+1/2at^2
A
v= ds/dt = u+at integrate with respect to time ∫v dt = ∫(u+at) dt ∫ds/dt dt = ∫u dt + ∫at dt s=ut+1/2at^2+c when t=0, s=0 so c=0 s=ut+1/2at^2
9
Q
how to derive v^2=u^2+2as
A
combine EOM 1&2 v=u+at v^2=u^2+2uat+a^2t^2 v^2=u^2+2a(ut+1/2at^2) v^2=u^2+2as
