Velocity and acceleration. A particle moves along x-axis, and its position is gi
ID: 1653356 • Letter: V
Question
Velocity and acceleration. A particle moves along x-axis, and its position is given by the equation: x(t) = At^3 - Bt^4 where A and B are positive constants. a) What are the SI units for A and B? b) What is the equation of the velocity as a function of time? c) At what time (in terms of A and B) is the velocity equal to zero? d) What is the maximum value of "x" in terms of A and B? e) What is the equation of the acceleration as a function of time? Motion with Constant Acceleration A train starts from rest and accelerates with the constant acceleration on the straight tracks. At a certain time t_1 the train had a velocity v_1 = 30.0 m/s. After travelling additional 200 m the train reaches a velocity v_2 = 50.0 m/s. a) Find the train's constant acceleration? b) Find the time it took to the train to travel additional 200 m? c) Find the time needed to reach the velocity v_1 starting from rest? d) Calculate the distance traveled by the train from the start to the point at which the velocity was equal to v_1?Explanation / Answer
Problem 2.
a)
The dimensions of A is meters/second2.
The dimension of B is meters/second3
b)
v = dx/dt
=> v(t) = d/dt(At^3 - Bt^4)
=> v = 3At^2 - 4Bt^3
c)
0 = 3At^2 - 4Bt^3
=> 3A(t^2) = 4Bt^3
=> A = 4/3*B*t
=> t = 3AB/4
d)
dx/dt = 0
e)
a = dv/dt
= d/dt(3At^2 - 4Bt^3)
= 6At - 12Bt^2
Pls post other question separately.
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