Question

The instantaneous speed of an object is the magnitude of the instantaneous acceleration, True or False

Answer 1

Answer:

False.

Explanation:

Instantaneous acceleration of an abject is the rate at which it's instantaneous speed changes at the time we calculate the acceleration.

Mathematically we can write

For a particle with instantaneous acceleration given by a(t)

$a(t)=\frac{dv(t)}{dt}\\\\dv=a(t)dt\\\\\int dv=\int a(t)dt\\\\\therefore v(t)=v_{o}+\int a(t)dt$

This is the relation between the instantaneous acceleration and speed of the object and we can see that they are not equal.