Question

What net force is needed to increase the velocity of a 5 kg object by 3 m/s over the course of 2.5 seconds?

Answer 1

Hi there!

Recall Newton's Second Law:

$\large\boxed{\Sigma F = ma}$

∑F = net force (N)

m = mass (kg)

a = acceleration (m/s²)

We must begin by solving for the acceleration using the following:

a = Δv/t

In this instance:

Δv = 3 m/s

t = 2.5 sec

a = 3/2.5 = 1.2 m/s²

Now, plug this value along with the mass into the equation for net force:

$\Sigma F = 5(1.2) = \boxed{6 N}}$

Answer 2

Answer:

$\boxed {\boxed {\sf 6 \ Newtons}}$

Explanation:

According to Newton's Second Law of Motion, force is the product of mass and acceleration. The mass of the object is 5 kilograms, but the acceleration is unknown.

We can find acceleration using the following formula:

$a= \frac{ \Delta v}{t}$

The velocity of the object increases by 3 meters per second. It accelerates in 2.5 seconds.

• Δv= 3 m/s
• t= 2.5 s

Substitute the values into the formula.

$a= \frac{3 \ m/s}{2.5 \ s}$

$a= 1.2 \ m/s/s = 1.2 \ m/s^2$

Now we know the mass and acceleration.

• m= 5 kg
• a= 1.2 m/s²

Substitute the values into the force formula.

$F=ma$

$F= (5 \ kg)(1.2 \ m/s^2)$

$F= 6 \ kg*m/s^2$

Convert the units. 1 kilogram meter per second squared is equal to 1 Newton. Our answer of 6 kilogram meters per second squared is equal to 6 Newtons.

$F= 6 \ N$