A 1000 kg sports car is initially traveling at 30 m/s. A frictional force f, defined as a function of velocity v, f=-200v, acts on it. What would the frictional force on the car be at 5 seconds?
To find the frictional force on the car at 5 seconds, we need to calculate its velocity at that time and then substitute the value into the given function f = -200v.
First, we need to know how the car's velocity changes over time. We can use the equation of motion:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the initial velocity (u) is 30 m/s, and the acceleration (a) is the force divided by mass:
a = f / m
Where:
f = force acting on the car
m = mass of the car
Here, the force acts opposite to the motion of the car, so we have f = -200v and m = 1000 kg.
We can now calculate the acceleration:
a = f / m = (-200v) / 1000
Since the frictional force (f) is given as a function of velocity, we substitute t = 5 seconds into the equation to find the acceleration at 5 seconds:
a(5) = (-200v) / 1000
Next, we substitute the initial velocity and time into the equation of motion and solve for the final velocity:
v = u + at
v(5) = 30 + a(5) * 5
To calculate the frictional force at 5 seconds, we substitute the final velocity into the function f = -200v:
f(5) = -200 * v(5)
By plugging in the values and calculating the expression, we can determine the frictional force on the car at 5 seconds.