Chapter 2, Problem 1RWDT

To determine

To prove : An object be at rest and have negative acceleration. Also, the motion of such an object.

Explanation of Solution

Given information :

An object is said to be “at rest” if its velocity is zero.

Formula used :

Velocity is the derivative of the positive function with respect to time. At time $t$ the velocity is:

  $v\left(t\right)=\frac{ds}{dt}=\underset{\Delta t\to 0}{\lim }\frac{f\left(t+\Delta t\right)-f\left(t\right)}{\Delta t}$ .

The acceleration is the derivative of velocity with respect to time. If velocity at time $t$ is : $v(t)=\frac{ds}{dt}$ , then the acceleration at time $t$ is: $a\left(t\right)=\frac{dv}{dt}=\frac{d^{2}s}{d{t}^2}$ .

Proof:

Yes, an object can be at rest and have negative acceleration.

When an object is thrown, and it reaches maximum height its velocity becomes zero while an $(-g)$ acceleration acts on the body.

Which is negative acceleration.