Properties of a velocity time graph
velocity
Gradient =
vu
t
Gradient = Acceleration
v
u
Area under graph =
t
time
1
u  v .t
2
Area = Distance travelled
Example
7
6
5
4
3
2
1
0
1
2
3
4
5
6
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9 10
11
The velocity-time graph shown is for a body which starts from rest,
accelerates uniformly to a velocity of 6 m/s in 2 seconds. The body then
maintains this velocity for a further 6 seconds before it retards
uniformly to rest. If the entire journey takes 11 seconds, find
a)The acceleration of the body during the first stage of the journey
b)The retardation of the body during the last stage of the journey
c)The total distance travelled by the body.
Example
A particle is initially at rest at a point A on a straight line ABCD. The
particle moves from A to B with uniform acceleration, reaching B with a
speed of 12m/s in 2 seconds. The acceleration then alters to a constant
1m/s2 and 8 seconds after leaving B the particle reaches C. The particle
then retards uniformly to come to rest at D after a further 10 seconds.
Draw a velocity-time graph for the motion and from it find
a) The acceleration of the particle when travelling from A to B
b) The speed of the particle when reaching C
c) The retardation of the particle when travelling from C to D
d) The total distance travelled from A to D.
Example
A train travels along a straight piece of track between two stations A
and B. The train starts from rest at A and accelerates at 1.25ms-2 until
it reaches a speed of 20ms-1. It then travels at this steady speed for a
distance of 1.56km and then decelerates at 2ms-2 to come to rest at B.
Find
a) The distance from A to B
b) The total time taken for the journey
c) The average speed for the journey.
A level Past paper question
A train, travelling along a straight horizontal track, has a steady
speed of 18m/s as it passes the point A. Fifteen seconds later, it
begins to slow down at a uniform rate for 30 s until its speed is
10m/s. The train then increases its speed for 45 s until it reaches
a speed of 20 m/s as it passes the point B.
a) Draw a sketch of the v-t graph for the motion of the train
between A and B.
b) Calculate the acceleration of the train just before it reaches B.
c) Find the distance from A to B.