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Pavlova-9 [17]
2 years ago
4

a particle moves along the x-axis. it is position as a function of time is given by x=6,8t+8,5t^2 , where t is in seconds and x

is in meters . what is the acceleration as a function of time ?
Physics
2 answers:
Lerok [7]2 years ago
8 0

Answer:

17 m/s²

Explanation:

A particle moves along the x-axis. Its position as a function of time is given by x = 6.8 t + 8.5 t²

where t is in seconds and x is in meters.

The first derivative of x is the object's velocity.

f'(x) = v = 6.8 + 2 × 8.5 t = 6.8 + 17 t

The second derivative of x is the acceleration.

f''(x) = a = 17

The acceleration of the particle is 17 m/s².

sertanlavr [38]2 years ago
4 0
To answer this question you simply need to consider the definition of acceleration which, for one-dimensional motion, is simply a \equiv \frac{d^2 x}{dt^2}. So take your second derivative and you are done!
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grigory [225]
<h2>Answer:</h2>

(c) 5m/s²

<h2>Explanation:</h2>

Total acceleration (a) of a particle in a circular motion is the vector sum of the radial or centripetal acceleration (a_{C}) of the particle and the tangential acceleration (a_{T}) of the particle and its magnitude can be calculated as follows;

a = \sqrt{(a_{C})^2 + (a_{T})^2}           ---------------------(i)

<em>But;</em>

a_{C} = \frac{v^{2} }{r}      ------------------------------(ii)

Where;

v = instantaneous velocity

r =  radius of the circular path of motion

<em>From the question;</em>

v = 30m/s

r = 300m

(i) First let's calculate the centripetal acceleration by substituting the values above into equation (ii) as follows;

a_{C} = \frac{30^{2} }{300}

a_{C} = \frac{900}{300}

a_{C} = 3m/s²

(ii) From the question, the velocity of the particle is increasing at a constant rate of 4m/s²  and that is the tangential acceleration a_{T}, of the particle. i.e;

a_{T} = 4m/s²

(iii) Now substitute the values of a_{C} and a_{T} into equation (i) as follows;

a = \sqrt{(3)^2 + (4)^2}

a = \sqrt{(9) + (16)}

a = \sqrt{25}

a = 5m/s²

Therefore, the magnitude of its total acceleration a, is 5m/s²

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elena55 [62]

Answer:

Answer:

15.67 seconds

Explanation:

Using first equation of Motion

Final Velocity= Initial Velocity + (Acceleration * Time)  

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v=3

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Explanation:

When you look at the graph, you can see that the first point on the graph is twenty on the y-axis.

The runner starts at twenty, and ends at thirty.

Therefore, the runner starts at twenty on the y-axis, so it's the starting position of the runner.

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