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What shape do you expect for a graph showing the position of motorcycle versus time if is speeding up with constant acceleration?

A parabola.

The equation of motion for an object moving with constant acceleration is:

```

s = ut + 1/2at^2

```

where:

* s is the position of the object

* u is the initial velocity of the object

* a is the acceleration of the object

* t is the time

If the object is speeding up with constant acceleration, then a is positive. This means that the graph of s versus t will be a parabola that opens upwards.