A particle is moving in x - axis according to relation #x= (4t - t^2 - 4)# m then? **The question has multiple answers**.
A: magnitude of x coordinate of particle is 4m
B: magnitude of a average velocity is equal to average speed, for time interval t=0 to t=2sec
C: average acceleration is equal to instantaneous acceleration during interval t=0 to t=2sec
D: distance traveled in interval t=0 to t=4sec is 8m.
The question has multiple answers.
A: magnitude of x coordinate of particle is 4m
B: magnitude of a average velocity is equal to average speed, for time interval t=0 to t=2sec
C: average acceleration is equal to instantaneous acceleration during interval t=0 to t=2sec
D: distance traveled in interval t=0 to t=4sec is 8m.
The question has multiple answers.
I got A,B, C, and D are correct.
I will consider each of the answer options below.
Now we calculate the average speed:
We can find the instantaneous acceleration by taking the derivative of the equation for velocity that we derived above, which is the second derivative of position.
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To find the velocity of the particle, differentiate the position function with respect to time:
v(t) = dx/dt = d(4t - t^2 - 4)/dt = 4 - 2t m/s
To find the acceleration of the particle, differentiate the velocity function with respect to time:
a(t) = dv/dt = d(4 - 2t)/dt = -2 m/s^2
To find the time(s) when the particle is at rest (velocity = 0), set v(t) = 0:
0 = 4 - 2t
Solve for t:
t = 2 s
To find the displacement of the particle at t = 2 s, substitute t = 2 into the position function:
x(2) = 4(2) - (2^2) - 4 = 4 m
Therefore, at t = 2 s, the particle is at rest and its displacement is 4 meters.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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