Graphically, slope of the plot yields acceleration and area under the plot yields displacement.

Since the plot involves regular geometric shapes, we shall find areas of these geometric shapes individually and then add them up to get various points for displacement – time plot.

The displacement between times 0 and 1 s is :

Δ
x
=
1
2
x
1
x
10
=
5
m
Δ
x
=
1
2
x
1
x
10
=
5
m

The velocity between 0 and 1 s is increasing at constant rate. The acceleration is constant and its magnitude is equal to the slope, which is
10
1
=
10
m
/
s
2
10
1
= 10 m /
s
2
. Since acceleration is in the direction of motion, the particle is accelerated. The resulting displacement – time curve is a parabola with an increasing slope.

The displacement between times 1 and 2 s is :

Δ
x
=
1
x
10
=
10
m
Δ
x
=
1
x
10
=
10
m

The velocity between 1 and 2 s is constant and as such acceleration is zero. The resulting displacement – time curve for this time interval is a straight line having slope equal to that of the magnitude of velocity.

The displacement at the end of 2 s is 5 + 10 = 15 m

Now, the displacement between times 2 and 4 s is :

Δ
x
=
1
2
x
(
20
+
30
)
x
1
=
25
m
Δ
x
=
1
2
x
(
20
+
30
)
x
1
=
25
m

The velocity between 2 and 4 s is increasing at constant rate. The acceleration, therefore, is constant and its magnitude is equal to the slope of the plot,
20
2
=
10
m
/
s
2
20
2
= 10 m /
s
2
. Since acceleration is in the direction of motion, the particle is accelerated and the resulting displacement – time curve is a parabola with increasing slope.

The displacement at the end of 4 s is 5 + 10 + 25 = 40 m

Now, the displacement between times 4 and 5 s is :

Δ
x
=
1
2
x
30
x
1
=
15
m
Δ
x
=
1
2
x
30
x
1
=
15
m

The velocity between 2 and 4 s is decreasing at constant rate, but always remains positive. As such, the acceleration is constant, but negative and its magnitude is equal to the slope, which is
30
1
=
30
m
/
s
2
30
1
= 30 m /
s
2
. Since acceleration is in the opposite direction of motion, the particle is decelerated. The resulting displacement – time curve is an inverted parabola with decreasing slope.

The final displacement at the end of 5 s is 5 + 10 + 25 + 15 = 55 m

Characteristics of motion : One dimensional, Unidirectional, variable acceleration in one dimension (magnitude)