Question

A 40kg body starts from rest accelerate to a velocity of 20 m/s in a time of 10 s. Determine the
acceleration of the body and the force it can exert.

Answer 1

Provided that:

• Initial velocity = 0 m/s
• Mass of body = 40 kg
• Final velocity = 20 m/s
• Time = 10 seconds

To determine:

• The acceleration
• The force

Solution:

• The acceleration = 2 m/s sq.
• The force = 80 Newton

Using concepts:

• Acceleration formula
• Force formula

Using formulas:

• ${\small{\underline{\boxed{\sf{a \: = \dfrac{v-u}{t}}}}}}$

• ${\small{\underline{\boxed{\sf{F \: = ma}}}}}$

Where, a denotes acceleration, v denotes final velocity, u denotes initial velocity, t denotes time taken, m denotes mass and F denotes force

Required solution:

~ Firstly let us calculate acceleration!

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{20-0}{10} \\ \\ :\implies \sf a \: = \dfrac{20}{10} \\ \\ :\implies \sf a \: = 2 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = 2 \: ms^{-2}$

Henceforth, acceleration = 2 m/s²

~ Now let us calculate force!

$:\implies \sf Force \: = Mass \times Acceleration \\ \\ :\implies \sf F \: = m \times a \\ \\ :\implies \sf F \: = ma \\ \\ :\implies \sf F \: = 40 \times 2 \\ \\ :\implies \sf F \: = 80 \: N \\ \\ :\implies \sf Force \: = 80 \: Newton$

Answer 2

Answer:-

• Initial velocity=u=0m/s
• Final velocity=20m/s=v
• Time=t=10s
• Mass=40kg=m
• Acceleration=a=?
• Force=F=?

We know that

$\boxed{\sf a=\dfrac{v-u}{t}}$

$\\ \sf\Rrightarrow a=\dfrac{20-0}{10}$

$\\ \sf\Rrightarrow a=\dfrac{20}{10}$

$\\ \sf\Rrightarrow a=2m/s^2$

According to Newtons 2nd law

$\boxed{\sf F=ma}$

$\\ \sf\Rrightarrow F=40\times 2$

$\\ \sf\Rrightarrow F=80N$