A car of mass 2000kg is travelling at 84m/h when a force of 500N beings to oppose the motion.Find the required to bring the car to rest.
Assuming 84mi/h.
Vo=84mi/h * 1600m/mi * 1h/3600s=37.3 m/s.
F = m*a.
a = F/m = -500/2000 = -0.25
V = Vo + at.
t = (V-Vo)/a = (0- 37.3)/-0.25 = 149.2s
Required to bring car to rest.
To find the time required to bring the car to rest, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Step 1: Convert the velocity from mph to m/s.
Given: velocity = 84 m/h
To convert m/h to m/s, we need to divide the velocity by 3.6 (since 1 hour = 3600 seconds).
velocity = 84 m/h ÷ 3.6 = 23.33 m/s
Step 2: Calculate the acceleration using Newton's second law.
Given: mass of the car (m) = 2000 kg
Force opposing the motion (F) = 500 N
Acceleration (a) = ?
According to Newton's second law, F = ma
Rearranging the equation, a = F/m
Substituting the values, a = 500 N / 2000 kg = 0.25 m/s²
Step 3: Determine the time required to bring the car to rest.
Given: initial velocity (u) = 23.33 m/s
final velocity (v) = 0 m/s (since the car is brought to rest)
acceleration (a) = -0.25 m/s² (negative sign indicates deceleration)
time (t) = ?
We can use the equation of motion, v = u + at, to find t.
Substituting the values, 0 = 23.33 m/s + (-0.25 m/s²) * t
Simplifying the equation, 0 - 23.33 m/s = -0.25 m/s² * t
-23.33 m/s = -0.25 m/s² * t
Dividing both sides by -0.25 m/s², t = (-23.33 m/s) / (-0.25 m/s²)
t = 93.32 s
Therefore, the time required to bring the car to rest is 93.32 seconds.
To find the time required to bring the car to rest, we can use the principles of Newton's second law of motion.
First, let's convert the car's initial velocity from miles per hour (mph) to meters per second (m/s) since the force is given in Newtons and the required answer needs to be in seconds.
1 mph = 0.44704 m/s
So, the car's initial velocity, v, is given by:
v = 84 mph * 0.44704 m/s = 37.54 m/s
Now that we have the initial velocity (v), we can calculate the acceleration (a) using Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
a = F / m
Given:
Mass (m) = 2000 kg
Force (F) = 500 N
a = 500 N / 2000 kg
a = 0.25 m/s^2
Now, we can use the kinematic equation to find the time (t) required to bring the car to rest:
v = u + at
where:
v = final velocity (0 m/s, as the car comes to rest)
u = initial velocity (37.54 m/s)
a = acceleration (-0.25 m/s^2, opposing the motion)
t = time
Plugging these values into the equation, we get:
0 = 37.54 m/s + (-0.25 m/s^2) * t
Simplifying the equation:
-37.54 m/s = -0.25 m/s^2 * t
To isolate the variable t, we can divide both sides of the equation by -0.25 m/s^2:
t = -37.54 m/s / (-0.25 m/s^2)
t = 150.16 s
Therefore, the time required to bring the car to rest is approximately 150.16 seconds.