When starting a foot race, a 76.6 kg sprinter exerts an average force of 524 N backward on the ground for 0.823 s.(a)What is his final speed (in m/s)? m/s(b)How far does he travel (in m)? m

(a) To find the final speed, we first need to find the acceleration. We can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.

The net force acting on the sprinter is 524 N (backward force exerted by the sprinter on the ground). The mass of the sprinter is 76.6 kg. So, the acceleration (a) can be calculated as:

a = F/m a = 524 N / 76.6 kg a = 6.84 m/s²

Next, we use the formula for final speed, which is v = u + at. Here, u is the initial speed, a is the acceleration, and t is the time. Since the sprinter is starting from rest, u = 0. So, the formula simplifies to v = at.

v = 6.84 m/s² * 0.823 s v = 5.63 m/s

So, the final speed of the sprinter is 5.63 m/s.

(b) To find the distance travelled, we can use the formula for distance in uniformly accelerated motion, which is d = ut + 0.5at². Here, d is the distance, u is the initial speed, a is the acceleration, and t is the time. Since the sprinter is starting from rest, u = 0. So, the formula simplifies to d = 0.5at².

d = 0.5 * 6.84 m/s² * (0.823 s)² d = 2.31 m

So, the sprinter travels a distance of 2.31 m.