1. Can the a cart move continiously, first toward a motion sensor and then away

Question

1. Can the a cart move continiously, first toward a motion sensor and then away and always have a positive acceleration?

2. Suppose an acceleration graph shows constant but negative values, that is, the graph is horizontal line in the negative region. What would a velocity graph look like which is correctly associated with this acceleration.

3. Suppose the acceleration graph is the same as in question 3. What would a position-time graph that is associated with this acceleration look like?

4. How is the shape of the position-time curve related to the direction of the acceleration?

Explanation / Answer

1.)

NO.

Since the velocity needs to change from positive to negative direction (hence decrease) in some time t making acceleration < 0 for that time interval

2.)

Let acceleration be -a

Hence v = -at

Thus, v vs t looks like the negative ramp funtion following v(t) = -at starting for v(0) = 0

3.)

x(t) = -at2/2

x vs t looks like the negative parabolic funtion following x(t) = -at2/2 starting for x(0) = 0

4.)

Shape is parabolic in the direction of acceleration

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