Explain.
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The velocity is the integral of acceleration. If acceleration is 100 m/s^2 then velocity is:
So to know the velocity at any time, t, we just put t in seconds into this equation. To know at what time we get to a certain velocity, we set this equation equal to that velocity and solve for t:
So to know the velocity at any time, t, we just put t in seconds into this equation. To know at what time we get to a certain velocity, we set this equation equal to that velocity and solve for t:
To solve this problem it is necessary to apply the concepts related to Normal Force, frictional force, kinematic equations of motion and Newton's second law.
From the kinematic equations of motion we know that the relationship of acceleration, velocity and distance is given by
Where,
Final velocity
Initial Velocity
a = Acceleration
x = Displacement
Acceleration can be expressed in terms of the drag coefficient by means of
Frictional Force
Force by Newton's second Law
Where,
m = mass
a= acceleration
Kinetic frictional coefficient
g = Gravity
Equating both equation we have that
Therefore,
Re-arrange to find x,
The distance traveled by the car depends on the coefficient of kinetic friction, acceleration due to gravity and initial velocity, therefore the three cars will stop at the same distance.