Relation between the acceleration and time for an object is given below. Calculate the velocity with which the object is moving at t 1 m/s.
A =3t -4t^2
Answers
Answer:
Let u be the initial velocity
∴v
1
=u+at
1
,v
2
=u+a(t
1
+t
2
)
and v
3
=u+a(t
1
+t
2
+t
3
)
Now v
1
=
2
u+v
1
=
2
u+(u+at
1
)
=u+
2
1
at
1
v
2
=
2
v
1
+v
2
=u+at
1
+
2
1
at
2
v
3
=
2
v
2
+v
3
=u+at
1
+at
2
+
2
1
at
3
So (v
1
−v
2
)=−
2
1
a(t
1
+t
2
)
and (v
2
−v
3
)=−
2
1
a(t
2
+t
3
)
∴(v
1
−v
2
):(v
2
−v
3
)=(t
1
+t
2
):(t
2
+t
3
)
Answer:
Let u be the initial velocity
∴v
1
=u+at
1
,v
2
=u+a(t
1
+t
2
)
and v
3
=u+a(t
1
+t
2
+t
3
)
Now v
1
=
2
u+v
1
=
2
u+(u+at
1
)
=u+
2
1
at
1
v
2
=
2
v
1
+v
2
=u+at
1
+
2
1
at
2
v
3
=
2
v
2
+v
3
=u+at
1
+at
2
+
2
1
at
3
So (v
1
−v
2
)=−
2
1
a(t
1
+t
2
)
and (v
2
−v
3
)=−
2
1
a(t
2
+t
3
)
∴(v
1
−v
2
):(v
2
−v
3
)=(t
1
+t
2
):(t
2
+t
3
)