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 ?

Question

Benjamin Asiedu · Accepted Answer

I am not sure about what you need but I think it is #t_1# or the velocity at this instant. I tried this but I am not sure, so have a look and check it!

The boat has a variable acceleration that can be described as linear from #t_0=0# up to #t_1# and then constant up to #t_2=1.4s#.
Graphically:

Axel Acevedo · Answer

undefined 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.