# In a water- tank test involving the launching of a small model boat, the model's initial horizontal velocity is 6 m/s and its horizontal acceleration varies linearly from -12 m/s2 at t=0 to -2 m/s2 at t=t1 and then remains equal to -2 m/s2 until t=1.4 ?

I am not sure about what you need but I think it is

The boat has a variable acceleration that can be described as linear from

Graphically:

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To find the time ( t_1 ), we can use the equation for acceleration, which is the rate of change of velocity with respect to time. The formula for acceleration when it varies linearly is:

[ a(t) = a_0 + bt ]

Given that the initial horizontal velocity ( v_0 = 6 ) m/s and the acceleration ( a(t) ) varies linearly from ( -12 ) m/s² at ( t = 0 ) to ( -2 ) m/s² at ( t = t_1 ), we can set up the equation:

[ -12 = 0 + b(0) ]

[ -2 = 0 + b(t_1) ]

Now, solve for ( t_1 ) by equating the two expressions for acceleration at ( t = t_1 ):

[ -12 = -2t_1 ]

[ t_1 = \frac{-12}{-2} ]

[ t_1 = 6 ]

So, ( t_1 = 6 ) seconds.

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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.

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