Question

Help on 2 simple physics problems, just can't think about them correctly.

Suppose an object starts at time t=0s at a position defined as x=0m. At t=0.5s, the object is at

x=1.5m, and at t=1.0s, the object is at x=2.0m. What is the average velocity for the first interval

(approximated at t=0.25s) and for the second interval (approximated at t=0.75s)? In the example above, what is the average acceleration of the object?

And,

he accepted value for the acceleration of gravity is a constant 9.81m/s. knowing that, what should

the graph of velocity vs. time for a falling object look like (assume down is the positive direction). What should the graph of position vs. time look like?

Answer 1

Suppose an object starts at time t=0s at a position defined as x=0m. At t=0.5s, the object is at

x=1.5m, and at t=1.0s, the object is at x=2.0m. What is the average velocity for the first interval

(approximated at t=0.25s) and for the second interval (approximated at t=0.75s)? In the example above, what is the average acceleration of the object?

v = dx / dt

Average velocity for the first interval is,

v = (1.5 - 0) / (0.5-0)

v₁ = 3 m/s

Average velocity for the second interval is,

v = (2 - 1.5 ) / (1-0.5)

v₂ = 1.0 m/s

Average acceleration of the obeject is,

a = dv / dt

a = (1.0 - 3.0)/ (1.0 - 0)

a = -2 m/s²

The accepted value for the acceleration of gravity is a constant 9.81m/s. knowing that, what should

the graph of velocity vs. time for a falling object look like (assume down is the positive direction). What should the graph of position vs. time look like?

g = 9.81 m/s²

The slope of the graph of velocity vs. time for a falling object should be,

slope = change in velocity / change in time = g = -9.81 m/s²

and since the slope has a constant value, the graph is linear with velocity increasing with increasing time.

Time in s Velocity in mis slope 9.81 m/sT

The object is 'falling'. Definitely, it's height will decrease with time. But change in the position is less initially, but increases with time as the velocity increases.