Question

Starting from rest, a particle that is confined to move along a straight line is accelerated at a rate of 5.0 m/s2. Which one of the following statements concerning the slope of the position versus time graph for this particle is true? a) The slope is not constant and decreases with increasing time. b) The slope has a constant value of 5.0 m/s. The slope has a constant value of 5.0 m/s2. c) The slope is not constant and increases with increasing time. d) The slope is both constant and negative.

Answer 1

c) The slope is not constant and increases with increasing time.

Step-by-step explanation:

The equation for the position of this particle (starting from rest is)

`s = at^2/2 = 5t^2/2 = 2.5t^2`

We can take derivative of this with respect to time t to get the equation of slope:

`s' = (2.5t^2)' = 2*2.5t = 5t`

As time t increase, the slope would increases with time as well.