Question

An object experiencing a constant force accelerates at $8\mathrm{m}/{\mathrm{s}}^2$.

What will the acceleration of this object be if

a. The force is halved? Explain.

b. The mass is halved?

c. The force is halved and the mass is halved?

Short answer

(a) When the force is halved, acceleration will be $4m/s^2$.

(b) When the mass is halved, acceleration will be $16m/s^2$.

(c) When both the force and mass is halved, acceleration will be$8m/s^2$.

Step-by-step solution

Part (a) Step-1: Given Information 

The expression for acceleration is $a=F/m$.

Part (a) Step 2: Calculation

When the force is halved, for the same mass, the acceleration becomes

$$\begin{gathered} a^{\text{'}}=(F/2)/m=F/2m \\ {a}^{\text{'}}=a/2 \end{gathered}$$

Therefore, the acceleration value is also halved. This value becomes

$a^{\text{'}}=4\mathrm{m}/{\mathrm{s}}^2\text{.}$

Part (b) Step-1: Given Information

The expression for acceleration is $a=F/m$.

Part (b) Step 2: Calculation

When the mass is halved, the acceleration becomes

$$\begin{gathered} a^{\text{'}\text{'}}=F/(m/2)=2F/m \\ {a}^{\text{'}\text{'}}=2a \end{gathered}$$

The acceleration value is doubled, and it becomes $a^{\text{'}\text{'}}=16\mathrm{m}/{\mathrm{s}}^2$.

Part (c) Step 1: Given information

The expression for acceleration is $a=F/m$.

Part (c) Step 2: Calculation

When both the force and the mass are halved,

$$\begin{gathered} a^{\text{'}\text{'}\text{'}}=(F/2)/(m/2)=F/m \\ {a}^{\text{'}\text{'}\text{'}}=a \end{gathered}$$

The acceleration value remains unchanged at $8\mathrm{m}/{\mathrm{s}}^2$