when starting a foot race a 66 kg sprinter exerts an average force of 640 N backward on the ground for 0.85s. What is his final speed in m/s?
To find the final speed of the sprinter, 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 the object's mass and acceleration.
In this case, the net force acting on the sprinter is the force exerted backward on the ground. The acceleration can be found using the formula:
acceleration = net force / mass
Given:
Mass (m) = 66 kg
Net force (F) = 640 N
Calculating the acceleration:
acceleration = 640 N / 66 kg
acceleration ≈ 9.70 m/s² (rounded to two decimal places)
Next, we can use kinematic equations to find the final speed of the sprinter. One of the relevant equations is:
final velocity = initial velocity + (acceleration * time)
In this case, the initial velocity is assumed to be zero because the sprinter starts from rest. Therefore, the equation can be rewritten as:
final velocity = acceleration * time
Given:
Time (t) = 0.85 s
Acceleration (a) ≈ 9.70 m/s²
Calculating the final velocity:
final velocity = (9.70 m/s²) * (0.85 s)
final velocity ≈ 8.25 m/s (rounded to two decimal places)
Therefore, the final speed of the sprinter is approximately 8.25 m/s.
To find the final speed of the sprinter, we can use Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by the acceleration it experiences. In this case, the force is exerted backward, and we need to calculate the acceleration.
First, we can calculate the acceleration using the equation:
F = m * a,
where F is the force, m is the mass, and a is the acceleration.
Given:
Force (F) = 640 N
Mass (m) = 66 kg
Rearranging the formula, the acceleration (a) can be found by dividing the force (F) by the mass (m):
a = F / m.
Substituting the given values:
a = 640 N / 66 kg.
Calculating the acceleration gives:
a ≈ 9.70 m/s².
Next, we can use the equation of motion:
v = u + at,
where v is the final velocity, u is the initial velocity (which is assumed to be 0 in this case), a is acceleration, and t is time.
Given:
Initial velocity (u) = 0 m/s
Acceleration (a) ≈ 9.70 m/s²
Time (t) = 0.85 s
Plugging in the values:
v = 0 + (9.70 m/s² * 0.85 s).
Calculating the final speed gives:
v ≈ 8.25 m/s.
Therefore, the sprinter's final speed is approximately 8.25 m/s.