Calculate a constant force required to bring an object of mass 2.0kg.moving with a velocity of 4.0m/s to rest in. 0.1sec and 2metre
a=changevelociy/time= (0-4)/.1=-40m/s^2
force=mass*acceleration=80N
you can have 0.1 s OR 2 m...not both (unless it is two different scenarios)
stopping in 0.1 s means traveling 0.2 m ... as bob said , 80 N
stopping in 2 m takes 1.0 s ... 8 n
V = Vo + a*t = 0,
4 + a*0.1 = 0,
a = -40 m/s^2.
F = M*a = 2 * (-40) = -80 N. The negative sign means the force
opposes the motion.
To calculate the constant force required to bring an object to rest in a given time and distance, we can use the equations of motion.
1. Start by calculating the acceleration of the object using the equation:
\(a = \frac{{v - u}}{{t}}\)
Where:
\(a\) is the acceleration,
\(v\) is the final velocity (0 m/s as the object comes to rest),
\(u\) is the initial velocity (4.0 m/s),
and \(t\) is the time taken to come to rest (0.1 s).
Plug in the values:
\(a = \frac{{0 - 4.0}}{{0.1}}\)
2. Calculate the deceleration (or negative acceleration) since the object is slowing down:
\(deceleration = -a\)
In this case, deceleration = -(-40 m/s^2) = 40 m/s^2.
3. Next, we need to calculate the force using Newton's second law of motion:
\(F = m \cdot a\),
where:
\(F\) is the force,
\(m\) is the mass of the object (2.0 kg),
and \(a\) is the acceleration (40 m/s^2).
Plug in the values:
\(F = 2.0 \cdot 40\)
Therefore, the constant force required to bring the object to rest is 80 N (Newton).