a body is moving with an acceleration of 2 metre per second square along a straight line it starts to move with initial velocity 4 meters per second calculate the distance travelled by the body during 15 second of its motion
Answers
Answer:
Displacement and Position from Velocity
To get our first two equations, we start with the definition of average velocity:
–
v
=
Δ
x
Δ
t
.
Substituting the simplified notation for
Δ
x
and
Δ
t
yields
–
v
=
x
−
x
0
t
.
Solving for x gives us
x
=
x
0
+
–
v
t
,
where the average velocity is
–
v
=
v
0
+
v
2
.
The equation
–
v
=
v
0
+
v
2
reflects the fact that when acceleration is constant, v is just the simple average of the initial and final velocities. (Figure) illustrates this concept graphically. In part (a) of the figure, acceleration is constant, with velocity increasing at a constant rate. The average velocity during the 1-h interval from 40 km/h to 80 km/h is 60 km/h:
–
v
=
v
0
+
v
2
=
40
km/h
+
80
km/h
2
=
60
km/h
.
In part (b), acceleration is not constant. During the 1-h interval, velocity is closer to 80 km/h than 40 km/h. Thus, the average velocity is greater than in part (a).
Graph A shows velocity in kilometers per hour plotted versus time in hour. Velocity increases linearly from 40 kilometers per hour at 1 hour, point vo, to 80 kilometers per hour at 2 hours, point v. Graph B shows velocity in kilometers per hour plotted versus time in hour. Velocity increases from 40 kilometers per hour at 1 hour, point vo, to 80 kilometers per hour at 2 hours, point v. Increase is not linear – first velocity increases very fast, then increase slows down.