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Sergeeva-Olga [200]
4 years ago
12

A particle moves in a straight line. Its speed(v)

Physics
1 answer:
Alina [70]4 years ago
3 0

Answer:

6v_0

Explanation:

The speed of the particle increases linearly with time, so we can write it as

v(t) = kt+v_0

where k is the a certain constant of proportionality and v_0 is the initial speed.

We also know that at t = 4 s, the speed is v=2v_0, so we can use this information to find k:

v(4) = 4k+v_0 = 2v_0 \rightarrow k = \frac{v_0}{4}

So the complete expression of v(t) is

v(t) = \frac{v_0}{4}t+v_0 = v_0 (\frac{t}{4}+1)

Now we integrate the quantity v(t), and we find:

\int {v(t)} \, dt =\int (\frac{v_0}{4}t+v_0) \, dt =\frac{v_0}{8}t^2 + v_0 t

Substituting the limit of integration t = 4, we find:

\frac{v_0}{8}4^2 + 4v_0 =2v_0+4v_0 = 6v_0

And substituting t = 0, we find 0. So, the result of the integration from 0 to 4 is

6v_0

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