2
1 Kinematics and Statics
v–t and a–t Graphs
The area under the v–t graph gives the displacement (see prob. 1.11) and the area
under the a–t graph gives the velocity.
Motion in Two Dimensions – Projectile Motion
Equation: y = x tan α −
1
2
gx 2
u 2 cos 2 α
(1.1)
Fig. 1.1 Projectile Motion
Time of flight: T =
2u sin α
g
(1.2)
Range: R =
u 2 sin 2α
g
(1.3)
Maximum height: H =
u 2 sin
2
α
2g
(1.4)
Velocity: v =
g 2 t 2 − 2ug sin α.t + u 2
(1.5)
Angle: tan θ =
u sin α − gt
u cos α
(1.6)
Relative Velocity
If v A is the velocity of A and v B that of B, then the relative velocity of A with respect
to B will be
v AB = v A − v B
(1.7)
Motion in Resisting Medium
In the absence of air the initial speed of a particle thrown upward is equal to that
of final speed, and the time of ascent is equal to that of descent. However, in the
presence of air resistance the final speed is less than the initial speed and the time of
descent is greater than that of ascent (see prob. 1.21).
1 Kinematics and Statics
v–t and a–t Graphs
The area under the v–t graph gives the displacement (see prob. 1.11) and the area
under the a–t graph gives the velocity.
Motion in Two Dimensions – Projectile Motion
Equation: y = x tan α −
1
2
gx 2
u 2 cos 2 α
(1.1)
Fig. 1.1 Projectile Motion
Time of flight: T =
2u sin α
g
(1.2)
Range: R =
u 2 sin 2α
g
(1.3)
Maximum height: H =
u 2 sin
2
α
2g
(1.4)
Velocity: v =
g 2 t 2 − 2ug sin α.t + u 2
(1.5)
Angle: tan θ =
u sin α − gt
u cos α
(1.6)
Relative Velocity
If v A is the velocity of A and v B that of B, then the relative velocity of A with respect
to B will be
v AB = v A − v B
(1.7)
Motion in Resisting Medium
In the absence of air the initial speed of a particle thrown upward is equal to that
of final speed, and the time of ascent is equal to that of descent. However, in the
presence of air resistance the final speed is less than the initial speed and the time of
descent is greater than that of ascent (see prob. 1.21).