Question

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

Answer 1

False.

Step-by-step 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)=(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.