A race car has a mass of 705 kg. It starts from rest and travels 39.0 m in 3.0 s. The car is uniformly accelerated during the entire time. What net force is exerted on it?
To calculate the net force exerted on the race car, we can use Newton's second law of motion, which states that the net force (F_net) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a):
F_net = m * a
First, let's calculate the acceleration of the race car using the formula:
a = (v_f - v_i) / t
Where:
v_f is the final velocity,
v_i is the initial velocity (which is 0 m/s as the car starts from rest), and
t is the time taken.
Given:
v_i = 0 m/s
t = 3.0 s
We can calculate the acceleration as follows:
a = (v_f - 0 m/s) / 3.0 s
Next, we need to find the final velocity of the car. We can use the formula:
v_f^2 = v_i^2 + 2 * a * d
Where:
v_i is the initial velocity,
a is the acceleration, and
d is the distance traveled.
Given:
v_i = 0 m/s
d = 39.0 m
We can calculate the final velocity as follows:
v_f^2 = 0^2 + 2 * a * 39.0 m
v_f^2 = 2 * a * 39.0 m
v_f^2 = 78.0 * a * m
Now that we have the final velocity, we can calculate the acceleration:
a = (v_f - v_i) / t
a = (sqrt(78.0 * a * m) - 0 m/s) / 3.0 s
We have a circular dependency here, so let's simplify the equation by substituting the value of acceleration again:
a = (sqrt(78.0 * [(v_f - 0 m/s) / 3.0 s] * m) - 0 m/s) / 3.0 s
Rearranging the equation, we have:
a = (sqrt(78.0 * m * v_f) - 0 m/s) / 3.0 s
Now we can substitute the given values:
m = 705 kg
v_f = (2 * a * d)^(1/2) = (2 * a * 39.0 m)^(1/2)
v_f = (2 * a * 39.0)^(1/2) m/s
Finally, we can substitute the calculated values of v_f and m into the equation for net force:
F_net = m * a
F_net = 705 kg * a
Thus, the net force exerted on the race car is 705 times the calculated acceleration.
To find the net force exerted on the race car, 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:
F = m * a
In this case, we are given the mass of the car (m = 705 kg), and we need to find the acceleration. We can use the kinematic equation:
d = v0 * t + (1/2) * a * t^2
where:
d = distance traveled (39.0 m)
v0 = initial velocity (0 m/s, since the car starts from rest)
t = time taken (3.0 s)
a = acceleration (unknown)
Rearranging the equation, we get:
39.0 m = (1/2) * a * (3.0 s)^2
Simplifying further:
39.0 m = 4.5 a
a = 8.67 m/s^2
Now, we can calculate the net force:
F = m * a
F = 705 kg * 8.67 m/s^2
F = 6111.35 N
Therefore, the net force exerted on the race car is 6111.35 Newtons.