Write difference between the following depending on the points given in brackets:
cytoplasm and protoplasm (location)
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Write difference between the following depending on the points given in brackets:
cytoplasm and protoplasm (location)
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Answer:
Protoplasm is the content of the cell including the cell membrane, cytoplasm and the cell nucleus whereas cytoplasm is the jelly like substance surrounding the nucleus within the cell membrane. The cytoplasm contains the cell organelles like mitochondria, ribosomes etc.
Explanation:
SoluTion:
Given acceleration:
\tt{a(t) = kt}a(t)=kt
We know that,
\large{\boxed{\tt{\blue{a(t) = \dfrac{d}{dt} [v(t)]}}}}
a(t)=
dt
d
[v(t)]
Using given expression,
\longrightarrow⟶ \tt{\dfrac{d}{dt} [v(t)] = kt}
dt
d
[v(t)]=kt
\longrightarrow⟶ \tt{d[v(t)] = kt.dt}d[v(t)]=kt.dt
Integrating it,
\longrightarrow⟶ \tt{v(t)}v(t) = \displaystyle\int kt.dt∫kt.dt
\longrightarrow⟶ \tt{v(t)}v(t) = k \displaystyle\int t.dtk∫t.dt
\longrightarrow⟶ \tt{v(t)}v(t) = \tt{k. \dfrac{t^{2}}{2} + c}k.
2
t
2
+c
\longrightarrow⟶ \tt{v(t)}v(t) = \tt{\dfrac{1}{2} kt^{2} + c}
2
1
kt
2
+c
Also, it is given that motion starts from rest, so \bold{\tt{v = 0}}v=0 at \bold{\tt{t = 0}}t=0 .
\longrightarrow⟶ \tt{v(0)=0}v(0)=0
\longrightarrow⟶ \tt{\dfrac{1}{2}k(0)^{2}\:+c=0}
2
1
k(0)
2
+c=0
\longrightarrow⟶ \tt{c = 0}c=0
Hence,
\large{\boxed{\boxed{\pink{\sf{v(t)=\dfrac{1}{2} kt^{2}\:m/s}}}}}
v(t)=
2
1
kt
2
m/s