The accelerated car will take 1.77 s to get to 10 m.
Explanation:
The motion of the car is a uniformly accelerated motion, so we can use one of the suvat equations, in particular:
[tex]s=ut+\frac{1}{2}at^2[/tex]
Where
s is the distance travelled
u is the initial velocity
a is the acceleration
t is the time taken
For the car in this problem,
u = 3 m/s
[tex]a=3 m/s^2[/tex]
s = 10 m
Substituting into the equation, we get:
[tex]10=3t+\frac{1}{2}(3)t^2\\1.5t^2+3t-10 = 0[/tex]
This is a quadratic equation, and solving for t, we find:
[tex]t=\frac{-3\pm \sqrt{3^2-4(1.5)(-10)}}{2(1.5)}[/tex]
We find two solutions:
t = -3.77 s
t = 1.77 s
We neglect the negative solution since it has no physical meaning: this means that the car will take 1.77 seconds to cover 10 m.
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