Sample problem on inertia

Answer 1

Problem:

A 2 kg block is moving with a velocity of 4 m/s towards the right. A force of 10 N is applied on the block in the opposite direction. Calculate the acceleration of the block and the time it will take to stop.

Solution:

Given:
Mass of the block (m) = 2 kg
Initial velocity (u) = 4 m/s
Force (F) = 10 N

Using Newton's second law of motion, we can calculate the acceleration:

F = ma

Where,
F = Force applied
m = Mass of the block
a = Acceleration

Rearranging the equation:

a = F/m

Substituting the given values:

a = 10 N / 2 kg
= 5 m/s²

Therefore, the acceleration of the block is 5 m/s².

To calculate the time it will take for the block to stop, we can use the equation:

v = u + at

Where,
v = Final velocity (zero in this case, since the block comes to rest)
u = Initial velocity
a = Acceleration
t = Time

Rearranging the equation:

t = (v - u) / a

Substituting the given values:

t = (0 - 4 m/s) / -5 m/s²
= 4/5 s
= 0.8 s

Therefore, it will take 0.8 seconds for the block to stop.