If the position-time graph is linear what can you say about the acceleration? If

Question

If the position-time graph is linear what can you say about the acceleration? If the velocity-time graph is linear what can you say about the acceleration? If the cart is speeding up toward the detector, what is the sign of its acceleration? If the cart is slowing down toward the detector, what is the sign of its acceleration? If the cart is speeding up away from the detector, what is the sign of its acceleration? If the cart is going away from the detector and is slowing down, what is the sign of its acceleration?

Explanation / Answer

Let x , v, a, and t denote position, velocity, acceleration and time respectively

1. if position time graph will be linear then dx/dt = constant So acceleration a = d2x/dt2 = 0

2. a = dv/dt = constant.

3. speeding up towards detector means negative acceleration.

4. speeding down towards detector means position acceleration.

5. speeding up away from the detector means positive  acceleration.

6. speeding up away from the detector means negative acceleration.

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