Answer to Question #223300 in Electric Circuits for Collins

Question

The magnitude of the acceleration of an object moving along a straight line is equal to the?

A. slope of the displacement time graph

B. Area below the force-time graph

C. Slope of its velocity-time graph

D. Area under its velocity-time graph

Answer 1

Acceleration ($\vec a$) is the derivative of velocity ($\vec v$) with respect to time (t).

i.e. $\vec a = \frac {d(\vec v)} {dt}$ (its unit is: $ms^{-2}$)

That is, $\frac {velocity \ (\vec v)} {time \ (t)} = \frac {ms^{-1}} {s} = ms^{-1-1} = ms^{-2}$ = acceleration $(\vec a)$

Therefore, the magnitude of the acceleration $|\vec a|$ of an object moving along a straight line is the slope/gradient ($m = \frac {d} {dt}$) of its velocity-time graph.

The answer is C.