Particle Acceleration and zero velocity

AI Thread Summary
To determine when the velocity of the particle is again zero, the acceleration function a_x = (10 - t) m/s^2 must be integrated to find the velocity function. Starting with the initial conditions of x_0 = 0 m and v_0x = 0 m/s at t = 0 s, the integration of the acceleration function yields the velocity function v_x = 10t - (t^2)/2 + C, where C is the constant of integration. Applying the initial condition v_x(0) = 0 allows for the determination of C, resulting in the complete velocity function. Setting the velocity function equal to zero will provide the time at which the velocity returns to zero. This approach effectively utilizes calculus to solve the problem.
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A particle's acceleration is described by the function a_x =(10 -t) m/s^2, where t is in s. Its initial conditions are x_0 =0 m and v_0x =0 m/s at t =0 s.

At what time is the velocity again zero?

I am having a hard time setting this problem up with where to begin if someone could help me with a formula that would be much appreciated.
 
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Ax = (10-t)m/s^2
Xi = 0 m
Vi = 0 m/s
t = 0 s

since acceleration is A = (Vf-Vi)/t
 
Last edited:
Hint. You are given a = f(t). How can you get v from this? Think calculus.
 
integration right?
 

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