Download ∆x = vt And the area under the graph is the displacement

From 10s to 20s, the velocity is constant. Displacement is then:
∆x = vt
And the area under the
graph is the displacement
Lets find the displacement for 0s to 10s:
Find the area under the graph:
∆x =
How can we determine the displacement of an accelerating body without a graph?
Find displacement using acceleration.
a=
vf - v i
t
An object moving at 13 m/s slows uniformly at the rate of 2.0 m/s each second for a time of 6.0 s. Determine its final velocity, average velocity during the 6.0 s, and the displacement during the 6.0 seconds.
Sometimes time is not given, but for constant
acceleration we can still find a formula to use.
∆x = vit + ½ a t2
Place to start
If we make substitutions to eliminate time we can get an
equation to use.
t= vf - vi
a
into
v = v + 2a∆x
2
f
2
i
∆x = vit + ½ a t2
Motion equation for
constant acceleration
Equations of Motion for uniform acceleration:
a=
vf = vi +at
∆x =
1
(vf + vi)
2
t
∆x = vit + ½ a t2
vf2 = vi2 + 2a∆x
Problems :
A truck starts from a stop and accelerates in a straight line to a velocity of 25 m/s in 12 s. Find the acceleration of the truck over the 12 s, find the position and velocity of the truck at times of 3s, 6s, and 8s.
vf - vi
t
An auto’s velocity increases uniformly from 4.0 m/s to 19.0 m/s while covering 80 m in a straight line. Find the acceleration and time taken.