Car A & B Velocity: Solving Mechanics Problem

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Car A travels at a constant velocity of 15 m/s, while Car B starts from rest and accelerates at 0.1 m/s² after being passed. To determine the speed of Car B when it passes Car A, one must use kinematic equations to find the point where their displacements are equal. An alternative method involves graphing the displacements of both cars over time to identify the crossing point. Understanding the relationship between their velocities and accelerations is crucial for solving the problem effectively.
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Homework Statement


Car A, which is traveling at a constant velocity of 15 ms-1, passes Car B, which is stationary, at time t = 0. At the instant that it is being passed, Car B begins to move, accelerating at a constant rate of 0.1 ms-2 in the direction in which Car A is travelling. At what speed will Car B be traveling as it passes Car A (in ms-1)?

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The Attempt at a Solution


Ok so I know that this is a relative velocity question? so the relative velocity will decrease by 0.1 per second. But I then get stuck, I am having trouble understanding the situation I think]

cheers
 
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Do you know the Kinematics Equations?

http://wiki.answers.com/Q/What_are_the_kinematic_equations

You need to find the right equation which will find the speed of the car in question as a function of time. Then you find the point where the displacement of both cars is equal, and calculate for the speed.

Alternatively, you could draw a graph and plot the displacement of the cars against time. That way, the speed of the car will be dx/dt at the point that they cross.
Hope that helps
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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